proyecto

1. LIBRERIAS NECESARIAS

library(sp)  

## Warning: package 'sp' was built under R version 3.6.3

library(sf) 

## Warning: package 'sf' was built under R version 3.6.3

## Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1

library(ncdf4)
library(raster)

## Warning: package 'raster' was built under R version 3.6.3

library(rasterVis)

## Loading required package: terra

## Warning: package 'terra' was built under R version 3.6.3

## terra version 1.2.5

## Loading required package: lattice

## Warning: package 'lattice' was built under R version 3.6.3

## Loading required package: latticeExtra

## Warning: package 'latticeExtra' was built under R version 3.6.3

library(RColorBrewer)

library(maptools)

## Checking rgeos availability: TRUE

library(maps)

## Warning: package 'maps' was built under R version 3.6.3

library(dplyr)

## Warning: package 'dplyr' was built under R version 3.6.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:terra':
## 
##     intersect, near, union

## The following objects are masked from 'package:raster':
## 
##     intersect, select, union

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(tidyr)

## Warning: package 'tidyr' was built under R version 3.6.3

## 
## Attaching package: 'tidyr'

## The following objects are masked from 'package:terra':
## 
##     expand, extract, pack, separate

## The following object is masked from 'package:raster':
## 
##     extract

library(ggplot2)

## 
## Attaching package: 'ggplot2'

## The following object is masked from 'package:latticeExtra':
## 
##     layer

library(ellipsis)

## Warning: package 'ellipsis' was built under R version 3.6.3

library(TSstudio)

## Warning: package 'TSstudio' was built under R version 3.6.3

library(astsa)

## 
## Attaching package: 'astsa'

## The following object is masked from 'package:maps':
## 
##     unemp

2. CARGA DATOS

2.1 Localización archivos

# set path and filename
data_path <- "./data/"

folder_fuel <- "fuel/"
fuel_path <- paste(data_path, folder_fuel, sep="")


wind_filename <- "adaptor.mars.internal-1627157739.9280307-9233-3-bfb7e7ba-55aa-4a70-b917-3f52ac1fb472.nc"
wind_file <- paste(data_path, wind_filename, sep="")


wave_filename <- "adaptor.mars.internal-1627158731.6650586-13503-5-7b2a701a-5196-4d19-961f-f557a6c22ae4.nc"
wave_file <- paste(data_path, wave_filename, sep="")

freak_wave_filename <- "adaptor.mars.internal-1627159551.019192-19965-5-64e8f8ba-76ac-4f6b-88ed-f0f67c8e67c1.nc"
freak_wave_file <- paste(data_path, freak_wave_filename, sep="")


max_indiv_wave_height_filename <- "adaptor.mars.internal-1627160342.4202654-24930-3-c4e15954-a6b6-41c3-ad02-c96804c4d58f.nc"
max_indiv_wave_height_file <- paste(data_path, max_indiv_wave_height_filename, sep="")

2.2 DATOS MESOCEÁNICOS

Guardamos los rasterbrick (cubos) de las variables:

u_wind_comp_10 <- brick(wind_file,varname="u10")

v_wind_comp_10 <- brick(wind_file,varname="v10")


u_wind_comp_10

## class      : RasterBrick 
## dimensions : 361, 481, 173641, 300  (nrow, ncol, ncell, nlayers)
## resolution : 0.25, 0.25  (x, y)
## extent     : -110.125, 10.125, -0.125, 90.125  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : D:/R/netcdf_M/data/adaptor.mars.internal-1627157739.9280307-9233-3-bfb7e7ba-55aa-4a70-b917-3f52ac1fb472.nc 
## names      : X1993.01.01, X1993.02.01, X1993.03.01, X1993.04.01, X1993.05.01, X1993.06.01, X1993.07.01, X1993.08.01, X1993.09.01, X1993.10.01, X1993.11.01, X1993.12.01, X1994.01.01, X1994.02.01, X1994.03.01, ... 
## Date/time  : 1993-01-01, 2017-12-01 (min, max)
## varname    : u10

raster::plot(u_wind_comp_10$X1993.01.01)

raster::plot(v_wind_comp_10$X1993.01.01)

mean_wave_direc <- brick(wave_file,varname="mwd")

mean_wave_period <- brick(wave_file,varname="mwp")

signif_wave_height <- brick(wave_file,varname="swh")


  

mean_wave_direc

## class      : RasterBrick 
## dimensions : 181, 241, 43621, 300  (nrow, ncol, ncell, nlayers)
## resolution : 0.5, 0.5  (x, y)
## extent     : -110.25, 10.25, -0.25, 90.25  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : D:/R/netcdf_M/data/adaptor.mars.internal-1627158731.6650586-13503-5-7b2a701a-5196-4d19-961f-f557a6c22ae4.nc 
## names      : X1993.01.01, X1993.02.01, X1993.03.01, X1993.04.01, X1993.05.01, X1993.06.01, X1993.07.01, X1993.08.01, X1993.09.01, X1993.10.01, X1993.11.01, X1993.12.01, X1994.01.01, X1994.02.01, X1994.03.01, ... 
## Date/time  : 1993-01-01, 2017-12-01 (min, max)
## varname    : mwd

raster::plot(mean_wave_direc$X1993.01.01)

raster::plot(mean_wave_period$X1993.01.01)

raster::plot(signif_wave_height$X1993.01.01)

bfi_index <- brick(freak_wave_file,varname="bfi")

peak_wave_period <- brick(freak_wave_file,varname="pp1d")

wave_spectral_kurtosis <- brick(freak_wave_file,varname="wsk")


peak_wave_period

## class      : RasterBrick 
## dimensions : 181, 241, 43621, 300  (nrow, ncol, ncell, nlayers)
## resolution : 0.5, 0.5  (x, y)
## extent     : -110.25, 10.25, -0.25, 90.25  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : D:/R/netcdf_M/data/adaptor.mars.internal-1627159551.019192-19965-5-64e8f8ba-76ac-4f6b-88ed-f0f67c8e67c1.nc 
## names      : X1993.01.01, X1993.02.01, X1993.03.01, X1993.04.01, X1993.05.01, X1993.06.01, X1993.07.01, X1993.08.01, X1993.09.01, X1993.10.01, X1993.11.01, X1993.12.01, X1994.01.01, X1994.02.01, X1994.03.01, ... 
## Date/time  : 1993-01-01, 2017-12-01 (min, max)
## varname    : pp1d

raster::plot(bfi_index$X1993.01.01)

raster::plot(peak_wave_period$X1993.01.01)

raster::plot(wave_spectral_kurtosis$X1993.01.01)

max_individual_wave_height <- brick(max_indiv_wave_height_file)


max_individual_wave_height

## class      : RasterBrick 
## dimensions : 181, 241, 43621, 300  (nrow, ncol, ncell, nlayers)
## resolution : 0.5, 0.5  (x, y)
## extent     : -110.25, 10.25, -0.25, 90.25  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=WGS84 +no_defs 
## source     : D:/R/netcdf_M/data/adaptor.mars.internal-1627160342.4202654-24930-3-c4e15954-a6b6-41c3-ad02-c96804c4d58f.nc 
## names      : X1993.01.01, X1993.02.01, X1993.03.01, X1993.04.01, X1993.05.01, X1993.06.01, X1993.07.01, X1993.08.01, X1993.09.01, X1993.10.01, X1993.11.01, X1993.12.01, X1994.01.01, X1994.02.01, X1994.03.01, ... 
## Date/time  : 1993-01-01, 2017-12-01 (min, max)
## varname    : hmax

raster::plot(max_individual_wave_height$X1993.01.01)

2.3 DATOS CONSUMO DE FUEL A VELOCIDAD FIJA, RUTA BIMINI – BISHOP ROCK

2.3.1. Unir archivos ‘nc’ de cada año.

Función de ayuda para dar formato largo:

files_fuel <- list.files(fuel_path)

getnc <- function(fl){
 
  nc <- nc_open(fl)
 
  dat <- ncvar_get(nc) %>% as.data.frame() %>%
    
    mutate(speed = nc$dim$speed$vals) %>%
   
    pivot_longer(cols = 1:12, names_to = "month", values_to = "fuel") %>%
   
    mutate(month = factor(month, levels = c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10","V11","V12")))
 
  nc_close(nc)
 
  return(dat)}

Unimos todos los archivos por año de consumo de fuel:

alldata <- list()

years <- 1993:2017

for(i in 1:length(files_fuel)){
 
  result <- getnc(paste(fuel_path,files_fuel[i],sep = ""))
 
  result$year <- years[i]
 
  alldata[[i]] <- result
 
}

alldata <- do.call("rbind", alldata)

2.3.2. Obtención del dataframe final.

Reorganizamos el dataframe del paso anterior:

fuel_fix_vel <- alldata %>%
  select(speed,year,month,fuel) %>%
  arrange(speed,year)

fuel_fix_vel

## # A tibble: 2,100 x 4
##    speed  year month   fuel
##    <dbl> <int> <fct>  <dbl>
##  1  5.14  1993 V1    74419.
##  2  5.14  1993 V2    72284.
##  3  5.14  1993 V3    74083.
##  4  5.14  1993 V4    82392.
##  5  5.14  1993 V5    79016.
##  6  5.14  1993 V6    70112.
##  7  5.14  1993 V7    70435.
##  8  5.14  1993 V8    72632.
##  9  5.14  1993 V9    81863.
## 10  5.14  1993 V10   83129.
## # ... with 2,090 more rows

2.3.3. Consumo de fuel por velocidades. Obtención de las series temporales y las tendencias.

Comprobamos los valores de velocidad:

speed_values <- unique(fuel_fix_vel$speed)

speed_values

## [1] 5.144440 5.658884 6.173328 6.687772 7.202216 7.716660 8.231104

Podemos filtrar los datos para una velocidad en particular, p, ejplo 6.687772:

fuel_speed <- fuel_fix_vel %>% 
  filter(speed==6.687772) %>%
  arrange(year) 

head(fuel_speed,24)

## # A tibble: 24 x 4
##    speed  year month    fuel
##    <dbl> <int> <fct>   <dbl>
##  1  6.69  1993 V1    118462.
##  2  6.69  1993 V2    113704.
##  3  6.69  1993 V3    116883.
##  4  6.69  1993 V4    123044.
##  5  6.69  1993 V5    121851.
##  6  6.69  1993 V6    111223.
##  7  6.69  1993 V7    111604.
##  8  6.69  1993 V8    113629.
##  9  6.69  1993 V9    122693.
## 10  6.69  1993 V10   124808.
## # ... with 14 more rows

Los datos de la columna fuel para cada velocidad a lo largo del tiempo forman nuestras series temporales. Las almacenamos en una lista, con las etiquetas de cada velocidad:

get_fuel_consump_speed_ts <- function(speed_vector) {
  
  fuel_consump_speed_ts <- list()
  
  for (v in 1:length(speed_vector)) {
    
    fuel_speed <- fuel_fix_vel %>%
      filter(speed==speed_vector[v]) %>%
      arrange(year) %>%
      select(fuel)
    
    lbl <- as.character(round(speed_vector[v],2))
    
    fuel_consump_speed_ts[[lbl]] <- ts(fuel_speed$fuel, start = 1993, frequency=12)
    
  }
  
  return(fuel_consump_speed_ts)
  

}



fuel_cons_speed_ts <- get_fuel_consump_speed_ts(speed_values)



str(fuel_cons_speed_ts)

## List of 7
##  $ 5.14: Time-Series [1:300] from 1993 to 2018: 74419 72284 74083 82392 79016 ...
##  $ 5.66: Time-Series [1:300] from 1993 to 2018: 87682 84794 87011 95237 91745 ...
##  $ 6.17: Time-Series [1:300] from 1993 to 2018: 101287 98758 100594 107780 105096 ...
##  $ 6.69: Time-Series [1:300] from 1993 to 2018: 118462 113704 116883 123044 121851 ...
##  $ 7.2 : Time-Series [1:300] from 1993 to 2018: 138978 133587 137287 143542 140673 ...
##  $ 7.72: Time-Series [1:300] from 1993 to 2018: 166930 160549 164553 172546 167334 ...
##  $ 8.23: Time-Series [1:300] from 1993 to 2018: 209477 197287 203615 212766 206718 ...

Para verificar representamos para una de las velocidades:

plot(fuel_cons_speed_ts$`5.14`)

Finalmente y a partir de estas series temporales obtenemos las tendencias para cada velocidad:

get_fuel_consump_speed_trends <- function(l) {
  
  
  get_trend_from_ts <- function(tseries) {
    
    tseries.dc <- stl(tseries, s.window = "periodic", na.action = na.omit)
    
    trend <- tseries.dc$time.series[,"trend"]
    
    return(trend) 
    
    
    }
  
  
  fuel_consump_speed_trends <- lapply(l,FUN = get_trend_from_ts)
  
  return(fuel_consump_speed_trends)

  
}



fuel_cons_speed_trends <- get_fuel_consump_speed_trends(fuel_cons_speed_ts)


str(fuel_cons_speed_trends)

## List of 7
##  $ 5.14: Time-Series [1:300] from 1993 to 2018: 76822 76815 76809 76784 76760 ...
##  $ 5.66: Time-Series [1:300] from 1993 to 2018: 89414 89411 89407 89385 89363 ...
##  $ 6.17: Time-Series [1:300] from 1993 to 2018: 102389 102500 102610 102703 102795 ...
##  $ 6.69: Time-Series [1:300] from 1993 to 2018: 118224 118350 118477 118579 118681 ...
##  $ 7.2 : Time-Series [1:300] from 1993 to 2018: 137940 138095 138251 138378 138505 ...
##  $ 7.72: Time-Series [1:300] from 1993 to 2018: 164659 165002 165345 165654 165964 ...
##  $ 8.23: Time-Series [1:300] from 1993 to 2018: 203656 204134 204611 205045 205478 ...

Representamos la tendencia correspondiente a la gráfica anterior:

plot(fuel_cons_speed_trends$`8.23`)

3. ESTABLECER PTOS RUTA BIMINI - BISHOP, EXTRACCIÓN DE DATOS MESOCEANICOS.

3.1 Obtener variable de clase SpatialPoints para la extraccion.

Observando el mapa con coordenadas se proponen los siguientes puntos intermedios (lat,lon) por orden desde Bimini hasta Bishop:

(30,-75) …… (35,-55) …… (40,-35) …… (45,-15)

Creamos la variable de clase SpatialPoints con dichos puntos:

latitude <- c(30,35,40,45)
longitude <- c(-75,-55,-35,-15)

mesoc_points <- data.frame(longitude,latitude)

mesoc_points

##   longitude latitude
## 1       -75       30
## 2       -55       35
## 3       -35       40
## 4       -15       45

coordinates(mesoc_points) <- ~ longitude + latitude
proj4string(mesoc_points) <- CRS("+proj=longlat +datum=WGS84")
mesoc_points <- spTransform(mesoc_points, CRS(proj4string(mean_wave_direc)))

raster::plot(mean_wave_direc$X1993.01.01)
raster::plot(mesoc_points, add = TRUE)
raster::text(mesoc_points,labels=c("1","2","3","4"), add=TRUE,pos=1)

## Warning in text.default(xy[, 1], xy[, 2], labels, ...): "add" is not a
## graphical parameter

3.2 Test de prueba del proceso de extraccion.

Probamos a realizar por un lado la extraccion con una de las variables, y las posteriores operaciones para obtener los datos de la serie temporal de dicha variable para los 4 puntos geográficos elegidos:

points_mean_wave_direc <- raster::extract(mean_wave_direc,mesoc_points,df=TRUE,along=TRUE,cellnumbers=TRUE)


points_mean_wave_direc

##   ID cells X1993.01.01 X1993.02.01 X1993.03.01 X1993.04.01 X1993.05.01
## 1  1 28991    86.08797  353.339036    17.06821    27.64311    90.98813
## 2  2 26621   296.61912  274.480497   255.45666    10.22886    36.09753
## 3  3 24251   292.33422  322.114241   327.67362   312.02826   357.25587
## 4  4 21881   279.39714    5.021062   302.82672   304.77690   329.05797
##   X1993.06.01 X1993.07.01 X1993.08.01 X1993.09.01 X1993.10.01 X1993.11.01
## 1    111.1161    138.4900    109.5890    96.21790    75.08458    70.56896
## 2    338.7100    253.2813    219.5185    26.20382    21.83103   324.89393
## 3    276.8647    236.3834    276.3812   307.67195   341.21498   304.43630
## 4    293.3505    317.7195    346.4557   301.18967    15.48060   299.03075
##   X1993.12.01 X1994.01.01 X1994.02.01 X1994.03.01 X1994.04.01 X1994.05.01
## 1    353.8554    93.49864    86.37363    29.31861    95.32247    85.38481
## 2    292.0815   288.34598   289.91710   289.07111   353.05887   222.75962
## 3    270.8274   287.25278   288.35696   268.43770   336.61147   310.50108
## 4    299.9207   297.39919   270.11320   298.89341   319.21370   298.67916
##   X1994.06.01 X1994.07.01 X1994.08.01 X1994.09.01 X1994.10.01 X1994.11.01
## 1    116.1976    127.7723    106.1336    96.17945    67.54207    80.74833
## 2    109.6879    167.3087    157.1898   322.01536   351.09771   324.64672
## 3    319.5598    298.3056    312.3853   243.51389   309.99568   296.19063
## 4    321.6253    288.0603    305.1999   320.52663   288.14272   273.34335
##   X1994.12.01 X1995.01.01 X1995.02.01 X1995.03.01 X1995.04.01 X1995.05.01
## 1    61.72999    335.7270    341.3194    45.09032    76.36456     60.4610
## 2   313.08850    280.8419    271.2888   355.21230   321.13641    298.0254
## 3   301.73902    275.3210    276.7603   320.13660   247.35382    266.0535
## 4   281.22097    284.1490    280.2761   320.81779   329.05797    277.5458
##   X1995.06.01 X1995.07.01 X1995.08.01 X1995.09.01 X1995.10.01 X1995.11.01
## 1  127.612992    129.5302    93.18002    78.82013    93.79529    36.19092
## 2   49.386201    167.3966   253.01208    97.22870    34.63628   342.85203
## 3  344.472601    301.6841   273.57957   240.56391   335.62814   342.93993
## 4    6.608671    298.7616   310.70434   324.93238   278.61707   289.29085
##   X1995.12.01 X1996.01.01 X1996.02.01 X1996.03.01 X1996.04.01 X1996.05.01
## 1    16.92538    67.66292    329.0360     11.7066    95.19612    98.66798
## 2   297.99798   321.60884    260.2525    287.0385   317.78540   349.93309
## 3   277.80953   323.66889    296.9652    305.8976   300.47003   326.41012
## 4   286.63751   293.98226    329.9040    295.3666   298.81650   319.86192
##   X1996.06.01 X1996.07.01 X1996.08.01 X1996.09.01 X1996.10.01 X1996.11.01
## 1    117.2633    160.4364    115.0495    96.77274     63.2352    39.02555
## 2    266.5644    198.6214    132.5406   303.35959    358.2447   325.90472
## 3    281.4517    286.3738    292.6748   293.05387    306.4469   301.17319
## 4    288.9503    317.0438    311.5723   326.17390    293.2626   307.11711
##   X1996.12.01 X1997.01.01 X1997.02.01 X1997.03.01 X1997.04.01 X1997.05.01
## 1    51.58908     24.2097    84.46191    101.5081    15.68935    103.1891
## 2    16.59577    302.6949   280.19918    287.0935   294.18003    279.3532
## 3   340.91284    302.1895   283.82486    285.1103   269.11889    322.3450
## 4   331.12351    299.0637   282.03400    289.9061    23.44062    318.8346
##   X1997.06.01 X1997.07.01 X1997.08.01 X1997.09.01 X1997.10.01 X1997.11.01
## 1    109.1879    136.9738    129.6895    99.00308    49.89709    4.054214
## 2    330.3984    245.6948    206.6528   334.39761   330.25005  314.181693
## 3    332.0354    252.8692    301.4698   340.87439   296.25655  303.227745
## 4    318.8786    303.9309    291.6970   302.61248   280.42991  289.274370
##   X1997.12.01 X1998.01.01 X1998.02.01 X1998.03.01 X1998.04.01 X1998.05.01
## 1    321.0870    70.90956    2.230388    88.38973    85.24198    142.5222
## 2    281.6604   304.14515  284.121510   316.59332   244.98065    232.6973
## 3    270.5582   305.50753  302.826722   297.91557   310.31430    249.0019
## 4    259.8075   292.03208  290.636747   324.72913   306.42494    351.3504
##   X1998.06.01 X1998.07.01 X1998.08.01 X1998.09.01 X1998.10.01 X1998.11.01
## 1    159.7058    146.9994    106.0951    99.86006    69.98665     77.7544
## 2    244.8049    212.8494    173.4998   329.64027   342.78062    309.9792
## 3    297.5530    290.0654    296.6411   302.95857   263.04862    299.4043
## 4    284.0171    312.1162    327.1133   301.68958   304.63407    308.0125
##   X1998.12.01 X1999.01.01 X1999.02.01 X1999.03.01 X1999.04.01 X1999.05.01
## 1    87.36245    82.24805    10.04208    2.812694    52.79214    77.34239
## 2   293.14176   332.91437   304.89226  273.936645   285.35204    28.79124
## 3   289.64243   300.32720   219.60089  322.295525   269.82205   344.47809
## 4   285.64869   290.29615   317.30747  322.015359   296.40487   316.07144
##   X1999.06.01 X1999.07.01 X1999.08.01 X1999.09.01 X1999.10.01 X1999.11.01
## 1    99.68976    139.7535    154.3002    94.48746    74.39241    61.82888
## 2   192.57858    255.8247    205.2630    63.44944    30.15362    31.14793
## 3   322.89980    288.8733    296.5532   321.97690   321.58687     7.64144
## 4   333.10115    308.1224    287.0495   297.72330   310.57249   325.57512
##   X1999.12.01 X2000.01.01 X2000.02.01 X2000.03.01 X2000.04.01 X2000.05.01
## 1    39.16838    42.61826    35.00434    13.37661    77.22703    111.8907
## 2   331.72229   280.36399   292.64186   319.14778   301.85987    264.6582
## 3   251.20473   300.90951   289.93908   202.74148   355.47599    310.5176
## 4   295.86102   336.38074   288.88433   343.07726   334.82060    314.2971
##   X2000.06.01 X2000.07.01 X2000.08.01 X2000.09.01 X2000.10.01 X2000.11.01
## 1    105.1173    147.0159   112.90701    85.06069    41.70086    21.18281
## 2    317.7579    209.6962    66.78946    78.16092    31.88405   284.84665
## 3    299.5087    350.2572   275.27155   333.86474   312.89073   319.28511
## 4    300.4700    335.0623   313.28077   304.24403   301.28856   311.01197
##   X2000.12.01 X2001.01.01 X2001.02.01 X2001.03.01 X2001.04.01 X2001.05.01
## 1    48.77643    342.0445    87.68107    23.92953    43.07971    84.41796
## 2   313.91801    283.7095   304.44180   298.40998   305.17792   326.65733
## 3   299.66799    280.2047   279.31474   285.05540   266.81713   280.42991
## 4   272.42595    294.2405   298.95384   268.55855   298.58028   300.25029
##   X2001.06.01 X2001.07.01 X2001.08.01 X2001.09.01 X2001.10.01 X2001.11.01
## 1    136.4025    129.4698    113.4454    86.71422    61.65308    61.83437
## 2    127.2339    187.5905    174.6974   334.54043   344.82968    24.13279
## 3    279.4576    281.3034    303.6398   349.06513   330.54120   131.99128
## 4    304.1506    297.1630    298.9044   344.40119   289.16999   345.31310
##   X2001.12.01 X2002.01.01 X2002.02.01 X2002.03.01 X2002.04.01 X2002.05.01
## 1    47.99636    358.2172    40.64062    85.76935     85.2255    92.61969
## 2   316.84602    287.6483   299.13512   349.66941    339.3637   311.44595
## 3   333.59007    279.7487   277.83150   319.43893    315.5221   298.08587
## 4    24.16026    263.9770   299.41529   305.72177    307.3588   296.04780
##   X2002.06.01 X2002.07.01 X2002.08.01 X2002.09.01 X2002.10.01 X2002.11.01
## 1    122.9985    133.1614    99.81062  86.5549136    56.37387    32.82344
## 2    255.3358    221.1171   149.35059  72.1730498    23.74276   299.79434
## 3    282.6932    279.5400   291.05425 338.4407877   332.46940   291.11468
## 4    297.6684    311.5338   313.86307   0.6592595   294.80628   286.98909
##   X2002.12.01 X2003.01.01 X2003.02.01 X2003.03.01 X2003.04.01 X2003.05.01
## 1    338.7484    321.3067    63.33408     77.3314    76.71614    107.8475
## 2    298.0254    278.6885   280.45188    337.5234   322.91629    334.2713
## 3    290.9499    274.7991   296.24007    312.0228   329.10741    286.4782
## 4    267.0973    290.4829   287.04403    303.6782   282.86900    295.7237
##   X2003.06.01 X2003.07.01 X2003.08.01 X2003.09.01 X2003.10.01 X2003.11.01
## 1    139.2262    130.2883    124.3773    85.91767    63.10885    61.42236
## 2    269.6572    248.5294    326.9650    73.27723    78.65533    16.01896
## 3    289.5435    299.0967    307.2929   319.13679    20.49063   312.84678
## 4    283.1656    287.3297    310.0726   309.63311   349.62546   293.68012
##   X2003.12.01 X2004.01.01 X2004.02.01 X2004.03.01 X2004.04.01 X2004.05.01
## 1    23.29779    335.1832    41.78875    53.46234    75.49659    111.4787
## 2   298.08038    287.0330   296.39389   314.25311   348.52677    333.7659
## 3   304.22206    262.0049   294.71838   299.11864   336.19396    333.1396
## 4   303.31564    282.2977   311.66569   294.88319   319.52133    331.8431
##   X2004.06.01 X2004.07.01 X2004.08.01 X2004.09.01 X2004.10.01 X2004.11.01
## 1    144.9833    146.2358    125.0915   111.72592    44.74423    43.46975
## 2    298.7176    182.8167    133.3646    52.73721    17.65601   347.47752
## 3    274.9749    296.0148    322.9163   317.57115    12.09663   307.66646
## 4    290.2083    299.9317    289.3293   316.82954   317.79089   341.88518
##   X2004.12.01 X2005.01.01 X2005.02.01 X2005.03.01 X2005.04.01 X2005.05.01
## 1    41.85467    55.80805   19.111773    316.5549    53.10527    74.51326
## 2   317.70300   331.22788  329.442509    298.7780   338.00131    28.76927
## 3   283.40736   292.25732  159.486015    285.4509   328.43171   355.55839
## 4   306.01842   313.90153    2.625916    238.2182   301.40941   315.48913
##   X2005.06.01 X2005.07.01 X2005.08.01 X2005.09.01 X2005.10.01 X2005.11.01
## 1   114.51110    119.7079    105.3425    74.51875   84.549803   69.426323
## 2    49.02363    175.8675    115.0604    72.87072    8.333615   26.286225
## 3   294.97658    304.5517    295.3666   300.70076  321.284729    5.235307
## 4   295.85553    349.1091    339.5230   305.40315  278.342396  334.293230
##   X2005.12.01 X2006.01.01 X2006.02.01 X2006.03.01 X2006.04.01 X2006.05.01
## 1    35.02631    62.31779    350.1748    359.9312    65.27876    109.9625
## 2   294.61950   273.97510    284.5335    286.8573   317.28549    103.3924
## 3   312.45675   282.42403    283.8963    273.4203   339.18790    301.6401
## 4   322.92727   302.53008    312.2260    275.0463   343.67056    273.4258
##   X2006.06.01 X2006.07.01 X2006.08.01 X2006.09.01 X2006.10.01 X2006.11.01
## 1    123.2347    128.6073    124.8608    76.88643     61.3015    61.07078
## 2    138.2813    195.6549    310.4516   102.00800    336.5346    63.83399
## 3    349.8067    301.6072    165.4409   309.66607    330.6291   355.39908
## 4    336.1006    295.9544    321.5100   278.34789    289.7193   315.92861
##   X2006.12.01 X2007.01.01 X2007.02.01 X2007.03.01 X2007.04.01 X2007.05.01
## 1    91.23534    46.15605    312.9731    71.60722    45.76601    91.26280
## 2   316.61529   288.75799    274.9419   330.40936   303.96936    54.31383
## 3   283.22608   274.19484    273.4972   269.23974   258.30777   296.00935
## 4   276.10107   296.11921    279.2928   302.81024   320.93315   302.37077
##   X2007.06.01 X2007.07.01 X2007.08.01 X2007.09.01 X2007.10.01 X2007.11.01
## 1    113.3630    125.9045    107.2872    86.79113   91.669320    51.87474
## 2    222.8860    127.8767    193.6992    25.81379    1.626108   349.03217
## 3    299.1846    305.2878    251.9409   239.80581  308.364124    22.65505
## 4    290.0160    288.9997    348.2411    28.64841  290.559839    24.77552
##   X2007.12.01 X2008.01.01 X2008.02.01 X2008.03.01 X2008.04.01 X2008.05.01
## 1     87.6536    55.58831    149.5429    62.94954     70.7008    84.12681
## 2    304.4308   270.17363    276.6394   300.15141    330.0578   260.94463
## 3    295.8061   298.98680    307.3698   279.71576    327.5692   296.49826
## 4    281.8692   281.63298    285.2092   312.79185    309.4628   286.73639
##   X2008.06.01 X2008.07.01 X2008.08.01 X2008.09.01 X2008.10.01 X2008.11.01
## 1    119.3618    124.9926    147.7630   86.868040     58.9558    55.50042
## 2    287.6977    140.7259    205.0762   50.885914    351.9712    26.03902
## 3    249.5567    307.1226    290.3511    3.823489    302.5081    70.54149
## 4    296.6741    309.1662    299.5361  351.322938    309.2266   338.60010
##   X2008.12.01 X2009.01.01 X2009.02.01 X2009.03.01 X2009.04.01 X2009.05.01
## 1    77.01278    358.0030    21.42452    56.42881    150.1416   113.44537
## 2   355.02553    269.7781   279.13345   356.99218    294.1471    45.99674
## 3   309.23758    283.5447   282.75364   327.38246    304.1012   340.17672
## 4   316.01101    276.0461   312.27546   324.10836    292.1420   311.42947
##   X2009.06.01 X2009.07.01 X2009.08.01 X2009.09.01 X2009.10.01 X2009.11.01
## 1    140.9896    150.0647    117.2523     73.3871    75.43616    52.33619
## 2    242.2779    227.6982    335.1337     66.7620   336.44666    86.17037
## 3    310.4407    304.8318    299.3109    313.9125   318.51053   310.72082
## 4    267.8005    281.2979    289.9171    356.5967   277.55683   285.46191
##   X2009.12.01 X2010.01.01 X2010.02.01 X2010.03.01 X2010.04.01 X2010.05.01
## 1    57.41763    331.0466    322.5153    346.6260    62.32329    108.6331
## 2   301.67859    291.6750    286.7639    314.3190   317.86231    299.9591
## 3   310.52855    273.9147    286.2969    313.0940   344.26934    272.6347
## 4   295.66875    294.9876    270.9372    274.3432   305.92503    329.3986
##   X2010.06.01 X2010.07.01 X2010.08.01 X2010.09.01 X2010.10.01 X2010.11.01
## 1    117.7193    125.7947    98.97561    86.59337     86.3956   48.023824
## 2    247.1725    208.6195   182.85517   168.47880    260.8622  353.470879
## 3    267.2456    299.1571   239.03124   308.28172    308.9300    6.487815
## 4    301.5303    302.1895   306.35352   304.13416    318.0546  320.389296
##   X2010.12.01 X2011.01.01 X2011.02.01 X2011.03.01 X2011.04.01 X2011.05.01
## 1  343.978190    329.0525    70.25034   45.167228    108.1222    70.62939
## 2  296.207110    284.8357   289.36776    3.191742     20.1775   102.36508
## 3    9.047765    289.9501   278.93020  305.776707    319.7081    21.01251
## 4   50.171765    312.3908   275.32100  334.040531    302.9531   322.10875
##   X2011.06.01 X2011.07.01 X2011.08.01 X2011.09.01 X2011.10.01 X2011.11.01
## 1    107.4136    130.6783    153.6080    91.30126    87.42288    57.08802
## 2    302.7169    198.9345    237.7787    11.08584   343.66506    23.06157
## 3    222.6223    278.3644    286.7034   310.63841   328.16803   312.66550
## 4    307.1226    312.5831    301.5248   286.48919   302.12905   280.23214
##   X2011.12.01 X2012.01.01 X2012.02.01 X2012.03.01 X2012.04.01 X2012.05.01
## 1    57.29678    35.30648    45.99674    100.0029    27.15419   111.05572
## 2   337.71016   291.95518   282.82505    317.0877   251.49039    35.69651
## 3   270.69551   268.08612   250.84766    286.9397   301.85438   351.51521
## 4   300.39312   298.61874   304.28249    290.7741   332.04091   316.86250
##   X2012.06.01 X2012.07.01 X2012.08.01 X2012.09.01 X2012.10.01 X2012.11.01
## 1    97.71761    144.7745    140.3523    82.00633    84.87392   26.879518
## 2   291.43330    217.2387    142.6870    89.32361    12.56907    8.459965
## 3   288.02736    296.0039    337.1553    16.06291   330.68403  331.568476
## 4   274.49148    306.4030    272.6622   349.14753   300.26128  322.328486
##   X2012.12.01 X2013.01.01 X2013.02.01 X2013.03.01 X2013.04.01 X2013.05.01
## 1    88.35677    45.87588    353.4379    333.4417   94.047985    92.03738
## 2   322.80092   308.23778    285.8465    306.0788    6.740514    39.65729
## 3   294.44920   255.87417    271.2998    326.8276  329.975374    37.35004
## 4   274.90349   277.46344    288.4778    293.0264  302.249910   333.13411
##   X2013.06.01 X2013.07.01 X2013.08.01 X2013.09.01 X2013.10.01 X2013.11.01
## 1    133.1888    137.5507    107.8091    77.97963    62.10904   62.098054
## 2    260.7853    321.8560    204.6752   174.10959   346.42827    8.811546
## 3    287.2363    272.8544    273.4697   321.60884   295.33914  289.961052
## 4    322.3889    335.0568    306.7600   315.98904   270.88228  335.677580
##   X2013.12.01 X2014.01.01 X2014.02.01 X2014.03.01 X2014.04.01 X2014.05.01
## 1    87.25258    326.5420    88.97203    17.23851    60.67525    83.64888
## 2   307.51813    262.5377   272.19522   290.01599   330.63459   301.18967
## 3   311.68217    292.3452   290.76859   283.97868   312.95665   281.48465
## 4   287.91749    290.8730   283.97868   295.65776   301.39842   308.90798
##   X2014.06.01 X2014.07.01 X2014.08.01 X2014.09.01 X2014.10.01 X2014.11.01
## 1    120.4001    145.7414    143.9395    94.86102    57.65934    54.86317
## 2    230.7251    192.1776    225.8030    50.50687    30.93918   285.59376
## 3    283.7095    335.4853    256.9564   346.37334   332.49138   314.73104
## 4    299.7943    308.9684    304.8923   315.41772   295.06447   294.89417
##   X2014.12.01 X2015.01.01 X2015.02.01 X2015.03.01 X2015.04.01 X2015.05.01
## 1    52.71523     46.8702    1.845846    71.60173    74.25507    88.93358
## 2    20.35329    257.0003  266.130447   290.07641   322.19664   351.99314
## 3    75.85366    279.5564  267.306046   269.75613   282.01202   337.44098
## 4   314.80795    296.8224  323.800732   301.33800   313.45656   301.62915
##   X2015.06.01 X2015.07.01 X2015.08.01 X2015.09.01 X2015.10.01 X2015.11.01
## 1    112.0610    171.4398    119.8727    83.84664     71.7116    78.69378
## 2    290.8840    274.0575    120.8396    67.56953    325.8608   345.03293
## 3    299.1955    274.0190    336.4027   333.71092    340.9238   267.65213
## 4    318.6424    280.7540    299.4867   332.52983    342.7037   285.88491
##   X2015.12.01 X2016.01.01 X2016.02.01 X2016.03.01 X2016.04.01 X2016.05.01
## 1    97.86594    21.29267    42.43698    71.09084   54.011689    109.7867
## 2   330.95321   272.60723   286.71991   301.10727    8.591808    298.3386
## 3   295.38309   280.66613   289.97204   264.36705  328.107600    309.2925
## 4   251.90789   278.03476   300.92049   306.62270  313.731229    302.1510
##   X2016.06.01 X2016.07.01 X2016.08.01 X2016.09.01 X2016.10.01 X2016.11.01
## 1    119.1311    137.2540   107.12790    105.4304    63.68566     42.8380
## 2    249.7490    215.8544    10.93202     80.0177     3.99928    302.6839
## 3    291.3674    269.4100   285.23668    293.6087   332.46940    313.9620
## 4    273.6070    301.9093   298.05291    287.4560   308.96291    338.5836
##   X2016.12.01 X2017.01.01 X2017.02.01 X2017.03.01 X2017.04.01 X2017.05.01
## 1    79.33651    346.4228     49.6389    58.31306    86.09896    136.0290
## 2   288.51627    301.7994    281.2649   291.76291   357.88762    318.6479
## 3   285.67616    305.3372    276.0297   280.95728    27.11574    293.2461
## 4   272.58526    296.1961    286.4178   293.11979    18.66131    256.1269
##   X2017.06.01 X2017.07.01 X2017.08.01 X2017.09.01 X2017.10.01 X2017.11.01
## 1    124.5476    127.7888    124.6575    69.87129    80.30886    61.29601
## 2    290.1368    195.6659    219.0296   222.84752    22.34742    13.17884
## 3    308.3147    269.8440    288.3899   280.95179   298.55831    11.61321
## 4    294.7074    301.2116    298.7561   296.60813   288.14821   330.98068
##   X2017.12.01
## 1    29.63174
## 2   302.39274
## 3   266.27328
## 4   297.33876

Comprobamos que los puntos siguen nuestro orden requerido:

# lonlat from cells
cells_lonlat <- xyFromCell(mean_wave_direc,points_mean_wave_direc$cells)

cells_lonlat

##        x  y
## [1,] -75 30
## [2,] -55 35
## [3,] -35 40
## [4,] -15 45

Damos formato para tener las series temporales en cada punto como columnas:

index <- points_mean_wave_direc$ID

df_aux <- points_mean_wave_direc %>%
  dplyr::select(-ID,-cells)

row.names(df_aux) <- index

df_aux <- as.data.frame(t(df_aux))

head(df_aux)

##                     1         2        3          4
## X1993.01.01  86.08797 296.61912 292.3342 279.397139
## X1993.02.01 353.33904 274.48050 322.1142   5.021062
## X1993.03.01  17.06821 255.45666 327.6736 302.826722
## X1993.04.01  27.64311  10.22886 312.0283 304.776899
## X1993.05.01  90.98813  36.09753 357.2559 329.057967
## X1993.06.01 111.11615 338.70997 276.8647 293.350513

Finalmente se obtiene con éxito como resultado las series temporales de la variable de prueba en forma de lista. Es decir de cada variable mesoceánica tendremos una lista con las series temporales (1993 - 2017) en cada uno de los puntos elegidos:

col_to_ts <- function(c) {
  
  c_ts <- ts(c, start = 1993, frequency=12)
  return(c_ts)

  
}


final_test <- lapply(df_aux,FUN = col_to_ts)

str(final_test)

## List of 4
##  $ 1: Time-Series [1:300] from 1993 to 2018: 86.1 353.3 17.1 27.6 91 ...
##  $ 2: Time-Series [1:300] from 1993 to 2018: 296.6 274.5 255.5 10.2 36.1 ...
##  $ 3: Time-Series [1:300] from 1993 to 2018: 292 322 328 312 357 ...
##  $ 4: Time-Series [1:300] from 1993 to 2018: 279.4 5.02 302.83 304.78 329.06 ...

3.3 OBTENCION DE LAS SERIES TEMPORALES DE LAS VARIABLES EN LOS PUNTOS ELEGIDOS MEDIANTE LA OPERACIÓN DE EXTRACCION.

3.3.1 FUNCIÓN PARA OBTENER A PARTIR DE LAS VARIABLES MESOCEÁNICAS (RasterBrick) Y LOS PUNTOS (SpatialPoints) LAS SERIES TEMPORALES DE LAS VARIABLES EN DICHOS PUNTOS, MEDIANTE LA OPERACIÓN DE EXTRACCION (raster::extract)

mesocvar_ts_from_points <- function(mesoc_rbrick,sp_points) {
  
  
  col_to_ts <- function(c) {
    
    c_ts <- ts(c, start = 1993, frequency=12)
    return(c_ts)
    
    
  }
  
  df_extract_points <- raster::extract(mesoc_rbrick,sp_points,df=TRUE,along=TRUE)
  
  index <- df_extract_points$ID
  
  df_aux <- df_extract_points %>%
    dplyr::select(-ID)
  
  row.names(df_aux) <- index
  
  df_aux <- as.data.frame(t(df_aux))
  
  
  l_mesoc_ts_points <- lapply(df_aux,FUN = col_to_ts)
  
  return(l_mesoc_ts_points)
  
  
}

3.3.2 OBTENCIÓN DE LAS VARIABLES (SERIES TEMPORALES EN CADA PUNTO)

Obtenemos la primera de las variables (u-component wind 10 meters) y observamos su estructura, con las series temporales correspondientes a cada punto:

u10.wind_pts_ts <- mesocvar_ts_from_points(u_wind_comp_10,mesoc_points)


str(u10.wind_pts_ts)

## List of 4
##  $ 1: Time-Series [1:300] from 1993 to 2018: -1.68 2.25 1.13 1.01 -1.54 ...
##  $ 2: Time-Series [1:300] from 1993 to 2018: 4.7748 1.7727 2.4426 0.0225 0.4191 ...
##  $ 3: Time-Series [1:300] from 1993 to 2018: 4.74 -2.03 2.95 1.17 1.53 ...
##  $ 4: Time-Series [1:300] from 1993 to 2018: 4.3882 -5.2959 -0.9756 4.8805 -0.0784 ...

Obtenemos el resto de variables:

v10.wind_pts_ts <- mesocvar_ts_from_points(v_wind_comp_10,mesoc_points)

m.wave.dir_pts_ts <- mesocvar_ts_from_points(mean_wave_direc,mesoc_points)

m.wave.period_pts_ts <- mesocvar_ts_from_points(mean_wave_period,mesoc_points)

sig.wave.height_pts_ts <- mesocvar_ts_from_points(signif_wave_height,mesoc_points)

bfi_pts_ts <- mesocvar_ts_from_points(bfi_index,mesoc_points)

peak.wave.period_pts_ts <- mesocvar_ts_from_points(peak_wave_period,mesoc_points)

wave.spectr.kurt_pts_ts <- mesocvar_ts_from_points(wave_spectral_kurtosis,mesoc_points)

max.indiv.wave.height_pts_ts <- mesocvar_ts_from_points(max_individual_wave_height,mesoc_points)

3.3.3 COMPROBACIÓN VARIABLES (SERIES TEMPORALES): MUESTRA DE OBTENCIÓN DE DATOS DE INTERÉS PARA EL POSTERIOR ANÁLISIS.

Procedemos a la descomposición en componentes (tendencia,estacional,residuos) de las series temporales en los puntos etiquetados como “1” y “3”, para la variable “mean wave direction”:

m.wave.dir.pt1.dc <- stl(m.wave.dir_pts_ts$`1`, s.window = "periodic", na.action = na.omit)

m.wave.dir.pt3.dc <- stl(m.wave.dir_pts_ts$`3`, s.window = "periodic", na.action = na.omit)


plot(m.wave.dir.pt1.dc)

plot(m.wave.dir.pt3.dc)

Mostramos los valores para cada punto:

boxplot(m.wave.dir_pts_ts$`1`)

boxplot(m.wave.dir_pts_ts$`3`)

3.3.4. OBTENCIÓN DE LAS VARIABLES TENDENCIAS EN CADA PUNTO.

Es de interés para el posterior análisis obtener la tendencia de las series temporales (trend component) para las variables en cada punto:

plot(m.wave.dir.pt3.dc$time.series[,"trend"])

3.3.4.1. FUNCIÓN PARA OBTENER LAS TENDENCIAS DE LAS VARIABLES EN TODOS LOS PUNTOS, A PARTIR DE LAS VARIABLES OBTENIDAS ANTERIORES.

get_mesoc_pts_trend_from_ts <- function(l) {
  
  
  get_trend_from_ts <- function(tseries) {
    
    tseries.dc <- stl(tseries, s.window = "periodic", na.action = na.omit)
    
    trend <- tseries.dc$time.series[,"trend"]
    
    return(trend) 
    
    
    }
  
  
  
  mesoc_pts_trend <- lapply(l,FUN = get_trend_from_ts)
  
  return(mesoc_pts_trend)

  
}

3.3.4.2. OBTENCIÓN DE LAS TENDENCIAS DE LAS VARIABLES MESOCEÁNICAS EN TODOS LOS PUNTOS.

Guardamos los datos de tendencia de todas las variables, para los puntos geográficos elegidos. De nuevo para cada variable se almacena en forma de lista las distintas tendencia de cada uno de los puntos:

u10.wind_pts_trend <- get_mesoc_pts_trend_from_ts(u10.wind_pts_ts)

v10.wind_pts_trend <- get_mesoc_pts_trend_from_ts(v10.wind_pts_ts)

m.wave.dir_pts_trend <- get_mesoc_pts_trend_from_ts(m.wave.dir_pts_ts)

m.wave.period_pts_trend <- get_mesoc_pts_trend_from_ts(m.wave.period_pts_ts)

sig.wave.height_pts_trend <- get_mesoc_pts_trend_from_ts(sig.wave.height_pts_ts)

bfi_pts_trend <- get_mesoc_pts_trend_from_ts(bfi_pts_ts)

peak.wave.period_pts_trend <- get_mesoc_pts_trend_from_ts(peak.wave.period_pts_ts)

wave.spectr.kurt_pts_trend <- get_mesoc_pts_trend_from_ts(wave.spectr.kurt_pts_ts)

max.indiv.wave.height_pts_trend <- get_mesoc_pts_trend_from_ts(max.indiv.wave.height_pts_ts)

Como muestra observamos la tendencia de la variable “mean wave direction” en los puntos etiquetados “1” y “3”:

str(m.wave.dir_pts_trend)

## List of 4
##  $ 1: Time-Series [1:300] from 1993 to 2018: 105 106 108 109 111 ...
##  $ 2: Time-Series [1:300] from 1993 to 2018: 164 169 174 180 185 ...
##  $ 3: Time-Series [1:300] from 1993 to 2018: 306 305 304 303 302 ...
##  $ 4: Time-Series [1:300] from 1993 to 2018: 235 240 245 249 254 ...

class(m.wave.dir_pts_trend$`1`)

## [1] "ts"

plot(m.wave.dir_pts_trend$`1`)

plot(m.wave.dir_pts_trend$`3`)

4. ANALISIS.

4.1. CONSUMO DE COMBUSTIBLE: tendencia a lo largo del tiempo

Pasamos a analizar las tendencias del consumo de fuel para las distintas velocidades.

fuel_speed_trends_df <- as.data.frame(fuel_cons_speed_trends) %>%
  mutate(year=as.character(floor(time(fuel_cons_speed_trends$`5.14`)))) %>%
  mutate(month=as.character(cycle(fuel_cons_speed_trends$`5.14`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything())

head(fuel_speed_trends_df,25)

##          date    X5.14    X5.66    X6.17    X6.69     X7.2    X7.72
## 1  1993-01-01 76821.84 89414.25 102388.6 118223.6 137939.6 164659.2
## 2  1993-02-01 76815.23 89410.58 102499.5 118350.0 138095.5 165001.9
## 3  1993-03-01 76808.62 89406.92 102610.4 118476.5 138251.3 165344.6
## 4  1993-04-01 76784.33 89384.82 102702.9 118579.0 138378.2 165654.3
## 5  1993-05-01 76760.03 89362.72 102795.4 118681.5 138505.1 165964.1
## 6  1993-06-01 76729.49 89334.77 102882.0 118776.4 138622.5 166263.9
## 7  1993-07-01 76698.95 89306.82 102968.7 118871.3 138739.8 166563.7
## 8  1993-08-01 76662.94 89273.57 103045.1 118963.2 138852.6 166847.9
## 9  1993-09-01 76626.93 89240.33 103121.6 119055.0 138965.3 167132.1
## 10 1993-10-01 76464.98 89073.17 103021.8 118971.9 138872.6 167108.4
## 11 1993-11-01 76303.04 88906.01 102922.1 118888.8 138779.9 167084.8
## 12 1993-12-01 76063.86 88652.77 102691.7 118650.7 138519.6 166813.3
## 13 1994-01-01 75824.69 88399.54 102461.3 118412.7 138259.3 166541.8
## 14 1994-02-01 75624.66 88184.36 102264.6 118201.2 138027.7 166275.2
## 15 1994-03-01 75424.63 87969.18 102068.0 117989.7 137796.1 166008.6
## 16 1994-04-01 75164.47 87715.14 101786.1 117718.6 137508.2 165607.6
## 17 1994-05-01 74904.31 87461.10 101504.2 117447.6 137220.2 165206.7
## 18 1994-06-01 74712.21 87284.28 101269.0 117278.2 137003.9 164853.4
## 19 1994-07-01 74520.10 87107.46 101033.8 117108.8 136787.5 164500.2
## 20 1994-08-01 74548.41 87144.84 101015.6 117189.6 136799.9 164385.4
## 21 1994-09-01 74576.71 87182.23 100997.5 117270.4 136812.2 164270.7
## 22 1994-10-01 74764.92 87385.17 101169.2 117510.5 137028.0 164391.3
## 23 1994-11-01 74953.12 87588.12 101340.9 117750.6 137243.8 164511.9
## 24 1994-12-01 75076.75 87729.44 101465.7 117910.2 137396.4 164621.8
## 25 1995-01-01 75200.38 87870.76 101590.6 118069.8 137549.1 164731.8
##       X8.23
## 1  203655.9
## 2  204133.6
## 3  204611.4
## 4  205044.5
## 5  205477.7
## 6  205896.3
## 7  206314.9
## 8  206731.5
## 9  207148.1
## 10 207232.5
## 11 207317.0
## 12 207040.1
## 13 206763.1
## 14 206421.4
## 15 206079.6
## 16 205543.9
## 17 205008.2
## 18 204646.3
## 19 204284.4
## 20 204284.3
## 21 204284.2
## 22 204472.2
## 23 204660.2
## 24 204810.9
## 25 204961.7

fuel_speed_df_long <- fuel_speed_trends_df %>%
  gather(key = "variable", value = "value", -date)

fuel_speed_df_long

##            date variable     value
## 1    1993-01-01    X5.14  76821.84
## 2    1993-02-01    X5.14  76815.23
## 3    1993-03-01    X5.14  76808.62
## 4    1993-04-01    X5.14  76784.33
## 5    1993-05-01    X5.14  76760.03
## 6    1993-06-01    X5.14  76729.49
## 7    1993-07-01    X5.14  76698.95
## 8    1993-08-01    X5.14  76662.94
## 9    1993-09-01    X5.14  76626.93
## 10   1993-10-01    X5.14  76464.98
## 11   1993-11-01    X5.14  76303.04
## 12   1993-12-01    X5.14  76063.86
## 13   1994-01-01    X5.14  75824.69
## 14   1994-02-01    X5.14  75624.66
## 15   1994-03-01    X5.14  75424.63
## 16   1994-04-01    X5.14  75164.47
## 17   1994-05-01    X5.14  74904.31
## 18   1994-06-01    X5.14  74712.21
## 19   1994-07-01    X5.14  74520.10
## 20   1994-08-01    X5.14  74548.41
## 21   1994-09-01    X5.14  74576.71
## 22   1994-10-01    X5.14  74764.92
## 23   1994-11-01    X5.14  74953.12
## 24   1994-12-01    X5.14  75076.75
## 25   1995-01-01    X5.14  75200.38
## 26   1995-02-01    X5.14  75321.77
## 27   1995-03-01    X5.14  75443.15
## 28   1995-04-01    X5.14  75654.41
## 29   1995-05-01    X5.14  75865.67
## 30   1995-06-01    X5.14  76158.07
## 31   1995-07-01    X5.14  76450.47
## 32   1995-08-01    X5.14  76723.02
## 33   1995-09-01    X5.14  76995.58
## 34   1995-10-01    X5.14  77150.15
## 35   1995-11-01    X5.14  77304.71
## 36   1995-12-01    X5.14  77351.91
## 37   1996-01-01    X5.14  77399.11
## 38   1996-02-01    X5.14  77336.40
## 39   1996-03-01    X5.14  77273.70
## 40   1996-04-01    X5.14  77220.57
## 41   1996-05-01    X5.14  77167.45
## 42   1996-06-01    X5.14  77124.96
## 43   1996-07-01    X5.14  77082.46
## 44   1996-08-01    X5.14  76761.23
## 45   1996-09-01    X5.14  76440.01
## 46   1996-10-01    X5.14  76080.01
## 47   1996-11-01    X5.14  75720.02
## 48   1996-12-01    X5.14  75572.99
## 49   1997-01-01    X5.14  75425.95
## 50   1997-02-01    X5.14  75301.65
## 51   1997-03-01    X5.14  75177.34
## 52   1997-04-01    X5.14  74796.93
## 53   1997-05-01    X5.14  74416.52
## 54   1997-06-01    X5.14  74186.98
## 55   1997-07-01    X5.14  73957.44
## 56   1997-08-01    X5.14  74301.95
## 57   1997-09-01    X5.14  74646.46
## 58   1997-10-01    X5.14  74933.39
## 59   1997-11-01    X5.14  75220.32
## 60   1997-12-01    X5.14  75174.80
## 61   1998-01-01    X5.14  75129.29
## 62   1998-02-01    X5.14  75058.45
## 63   1998-03-01    X5.14  74987.61
## 64   1998-04-01    X5.14  74787.85
## 65   1998-05-01    X5.14  74588.10
## 66   1998-06-01    X5.14  74438.36
## 67   1998-07-01    X5.14  74288.62
## 68   1998-08-01    X5.14  74336.73
## 69   1998-09-01    X5.14  74384.83
## 70   1998-10-01    X5.14  74661.07
## 71   1998-11-01    X5.14  74937.30
## 72   1998-12-01    X5.14  75225.60
## 73   1999-01-01    X5.14  75513.91
## 74   1999-02-01    X5.14  75921.21
## 75   1999-03-01    X5.14  76328.52
## 76   1999-04-01    X5.14  76686.94
## 77   1999-05-01    X5.14  77045.35
## 78   1999-06-01    X5.14  77041.55
## 79   1999-07-01    X5.14  77037.75
## 80   1999-08-01    X5.14  76902.04
## 81   1999-09-01    X5.14  76766.33
## 82   1999-10-01    X5.14  76857.31
## 83   1999-11-01    X5.14  76948.28
## 84   1999-12-01    X5.14  76976.67
## 85   2000-01-01    X5.14  77005.07
## 86   2000-02-01    X5.14  77010.10
## 87   2000-03-01    X5.14  77015.12
## 88   2000-04-01    X5.14  77166.79
## 89   2000-05-01    X5.14  77318.46
## 90   2000-06-01    X5.14  77528.11
## 91   2000-07-01    X5.14  77737.75
## 92   2000-08-01    X5.14  77798.11
## 93   2000-09-01    X5.14  77858.47
## 94   2000-10-01    X5.14  77794.69
## 95   2000-11-01    X5.14  77730.92
## 96   2000-12-01    X5.14  77641.65
## 97   2001-01-01    X5.14  77552.38
## 98   2001-02-01    X5.14  77339.67
## 99   2001-03-01    X5.14  77126.96
## 100  2001-04-01    X5.14  76888.87
## 101  2001-05-01    X5.14  76650.78
## 102  2001-06-01    X5.14  76477.74
## 103  2001-07-01    X5.14  76304.70
## 104  2001-08-01    X5.14  76302.03
## 105  2001-09-01    X5.14  76299.37
## 106  2001-10-01    X5.14  76355.50
## 107  2001-11-01    X5.14  76411.63
## 108  2001-12-01    X5.14  76444.16
## 109  2002-01-01    X5.14  76476.69
## 110  2002-02-01    X5.14  76471.87
## 111  2002-03-01    X5.14  76467.05
## 112  2002-04-01    X5.14  76326.24
## 113  2002-05-01    X5.14  76185.43
## 114  2002-06-01    X5.14  75795.19
## 115  2002-07-01    X5.14  75404.95
## 116  2002-08-01    X5.14  74942.50
## 117  2002-09-01    X5.14  74480.05
## 118  2002-10-01    X5.14  74246.90
## 119  2002-11-01    X5.14  74013.75
## 120  2002-12-01    X5.14  73989.09
## 121  2003-01-01    X5.14  73964.43
## 122  2003-02-01    X5.14  73985.91
## 123  2003-03-01    X5.14  74007.40
## 124  2003-04-01    X5.14  74158.09
## 125  2003-05-01    X5.14  74308.78
## 126  2003-06-01    X5.14  74483.10
## 127  2003-07-01    X5.14  74657.42
## 128  2003-08-01    X5.14  74712.46
## 129  2003-09-01    X5.14  74767.50
## 130  2003-10-01    X5.14  74684.74
## 131  2003-11-01    X5.14  74601.99
## 132  2003-12-01    X5.14  74577.43
## 133  2004-01-01    X5.14  74552.87
## 134  2004-02-01    X5.14  74699.82
## 135  2004-03-01    X5.14  74846.78
## 136  2004-04-01    X5.14  75181.64
## 137  2004-05-01    X5.14  75516.51
## 138  2004-06-01    X5.14  76070.38
## 139  2004-07-01    X5.14  76624.25
## 140  2004-08-01    X5.14  77257.43
## 141  2004-09-01    X5.14  77890.61
## 142  2004-10-01    X5.14  78245.85
## 143  2004-11-01    X5.14  78601.09
## 144  2004-12-01    X5.14  78664.65
## 145  2005-01-01    X5.14  78728.20
## 146  2005-02-01    X5.14  78626.38
## 147  2005-03-01    X5.14  78524.57
## 148  2005-04-01    X5.14  78259.11
## 149  2005-05-01    X5.14  77993.65
## 150  2005-06-01    X5.14  77454.33
## 151  2005-07-01    X5.14  76915.00
## 152  2005-08-01    X5.14  76423.36
## 153  2005-09-01    X5.14  75931.71
## 154  2005-10-01    X5.14  75840.81
## 155  2005-11-01    X5.14  75749.91
## 156  2005-12-01    X5.14  75726.89
## 157  2006-01-01    X5.14  75703.88
## 158  2006-02-01    X5.14  75650.79
## 159  2006-03-01    X5.14  75597.70
## 160  2006-04-01    X5.14  75663.07
## 161  2006-05-01    X5.14  75728.45
## 162  2006-06-01    X5.14  75634.76
## 163  2006-07-01    X5.14  75541.07
## 164  2006-08-01    X5.14  75024.43
## 165  2006-09-01    X5.14  74507.80
## 166  2006-10-01    X5.14  73938.91
## 167  2006-11-01    X5.14  73370.03
## 168  2006-12-01    X5.14  73141.90
## 169  2007-01-01    X5.14  72913.77
## 170  2007-02-01    X5.14  72861.86
## 171  2007-03-01    X5.14  72809.96
## 172  2007-04-01    X5.14  72795.76
## 173  2007-05-01    X5.14  72781.57
## 174  2007-06-01    X5.14  72985.12
## 175  2007-07-01    X5.14  73188.68
## 176  2007-08-01    X5.14  73667.17
## 177  2007-09-01    X5.14  74145.65
## 178  2007-10-01    X5.14  74572.80
## 179  2007-11-01    X5.14  74999.94
## 180  2007-12-01    X5.14  75259.78
## 181  2008-01-01    X5.14  75519.63
## 182  2008-02-01    X5.14  75781.47
## 183  2008-03-01    X5.14  76043.31
## 184  2008-04-01    X5.14  76358.20
## 185  2008-05-01    X5.14  76673.09
## 186  2008-06-01    X5.14  76819.91
## 187  2008-07-01    X5.14  76966.74
## 188  2008-08-01    X5.14  76833.15
## 189  2008-09-01    X5.14  76699.55
## 190  2008-10-01    X5.14  76461.00
## 191  2008-11-01    X5.14  76222.45
## 192  2008-12-01    X5.14  76103.09
## 193  2009-01-01    X5.14  75983.72
## 194  2009-02-01    X5.14  75904.57
## 195  2009-03-01    X5.14  75825.42
## 196  2009-04-01    X5.14  75944.62
## 197  2009-05-01    X5.14  76063.83
## 198  2009-06-01    X5.14  76356.56
## 199  2009-07-01    X5.14  76649.30
## 200  2009-08-01    X5.14  76852.47
## 201  2009-09-01    X5.14  77055.64
## 202  2009-10-01    X5.14  76970.99
## 203  2009-11-01    X5.14  76886.34
## 204  2009-12-01    X5.14  76684.87
## 205  2010-01-01    X5.14  76483.39
## 206  2010-02-01    X5.14  76294.82
## 207  2010-03-01    X5.14  76106.25
## 208  2010-04-01    X5.14  75955.56
## 209  2010-05-01    X5.14  75804.86
## 210  2010-06-01    X5.14  75573.66
## 211  2010-07-01    X5.14  75342.46
## 212  2010-08-01    X5.14  75214.30
## 213  2010-09-01    X5.14  75086.15
## 214  2010-10-01    X5.14  75222.56
## 215  2010-11-01    X5.14  75358.96
## 216  2010-12-01    X5.14  75632.18
## 217  2011-01-01    X5.14  75905.39
## 218  2011-02-01    X5.14  75904.98
## 219  2011-03-01    X5.14  75904.56
## 220  2011-04-01    X5.14  75836.73
## 221  2011-05-01    X5.14  75768.90
## 222  2011-06-01    X5.14  75761.54
## 223  2011-07-01    X5.14  75754.18
## 224  2011-08-01    X5.14  75721.76
## 225  2011-09-01    X5.14  75689.33
## 226  2011-10-01    X5.14  75488.86
## 227  2011-11-01    X5.14  75288.38
## 228  2011-12-01    X5.14  75258.35
## 229  2012-01-01    X5.14  75228.32
## 230  2012-02-01    X5.14  75504.05
## 231  2012-03-01    X5.14  75779.77
## 232  2012-04-01    X5.14  76160.33
## 233  2012-05-01    X5.14  76540.89
## 234  2012-06-01    X5.14  76911.27
## 235  2012-07-01    X5.14  77281.65
## 236  2012-08-01    X5.14  77780.56
## 237  2012-09-01    X5.14  78279.47
## 238  2012-10-01    X5.14  78620.29
## 239  2012-11-01    X5.14  78961.11
## 240  2012-12-01    X5.14  78969.64
## 241  2013-01-01    X5.14  78978.17
## 242  2013-02-01    X5.14  78717.58
## 243  2013-03-01    X5.14  78456.99
## 244  2013-04-01    X5.14  78034.48
## 245  2013-05-01    X5.14  77611.96
## 246  2013-06-01    X5.14  77304.55
## 247  2013-07-01    X5.14  76997.14
## 248  2013-08-01    X5.14  76741.51
## 249  2013-09-01    X5.14  76485.87
## 250  2013-10-01    X5.14  76260.03
## 251  2013-11-01    X5.14  76034.18
## 252  2013-12-01    X5.14  76019.14
## 253  2014-01-01    X5.14  76004.09
## 254  2014-02-01    X5.14  76138.81
## 255  2014-03-01    X5.14  76273.54
## 256  2014-04-01    X5.14  76478.59
## 257  2014-05-01    X5.14  76683.65
## 258  2014-06-01    X5.14  76767.84
## 259  2014-07-01    X5.14  76852.02
## 260  2014-08-01    X5.14  76604.88
## 261  2014-09-01    X5.14  76357.74
## 262  2014-10-01    X5.14  76171.29
## 263  2014-11-01    X5.14  75984.83
## 264  2014-12-01    X5.14  75923.36
## 265  2015-01-01    X5.14  75861.90
## 266  2015-02-01    X5.14  75848.72
## 267  2015-03-01    X5.14  75835.54
## 268  2015-04-01    X5.14  75815.88
## 269  2015-05-01    X5.14  75796.22
## 270  2015-06-01    X5.14  75908.62
## 271  2015-07-01    X5.14  76021.03
## 272  2015-08-01    X5.14  76342.91
## 273  2015-09-01    X5.14  76664.79
## 274  2015-10-01    X5.14  76916.72
## 275  2015-11-01    X5.14  77168.66
## 276  2015-12-01    X5.14  77120.41
## 277  2016-01-01    X5.14  77072.16
## 278  2016-02-01    X5.14  76933.01
## 279  2016-03-01    X5.14  76793.85
## 280  2016-04-01    X5.14  76613.20
## 281  2016-05-01    X5.14  76432.55
## 282  2016-06-01    X5.14  76256.71
## 283  2016-07-01    X5.14  76080.87
## 284  2016-08-01    X5.14  75929.87
## 285  2016-09-01    X5.14  75778.87
## 286  2016-10-01    X5.14  75698.99
## 287  2016-11-01    X5.14  75619.10
## 288  2016-12-01    X5.14  75610.06
## 289  2017-01-01    X5.14  75601.01
## 290  2017-02-01    X5.14  75522.64
## 291  2017-03-01    X5.14  75444.27
## 292  2017-04-01    X5.14  75254.71
## 293  2017-05-01    X5.14  75065.15
## 294  2017-06-01    X5.14  74896.92
## 295  2017-07-01    X5.14  74728.69
## 296  2017-08-01    X5.14  74541.31
## 297  2017-09-01    X5.14  74353.94
## 298  2017-10-01    X5.14  74145.30
## 299  2017-11-01    X5.14  73936.65
## 300  2017-12-01    X5.14  73717.80
## 301  1993-01-01    X5.66  89414.25
## 302  1993-02-01    X5.66  89410.58
## 303  1993-03-01    X5.66  89406.92
## 304  1993-04-01    X5.66  89384.82
## 305  1993-05-01    X5.66  89362.72
## 306  1993-06-01    X5.66  89334.77
## 307  1993-07-01    X5.66  89306.82
## 308  1993-08-01    X5.66  89273.57
## 309  1993-09-01    X5.66  89240.33
## 310  1993-10-01    X5.66  89073.17
## 311  1993-11-01    X5.66  88906.01
## 312  1993-12-01    X5.66  88652.77
## 313  1994-01-01    X5.66  88399.54
## 314  1994-02-01    X5.66  88184.36
## 315  1994-03-01    X5.66  87969.18
## 316  1994-04-01    X5.66  87715.14
## 317  1994-05-01    X5.66  87461.10
## 318  1994-06-01    X5.66  87284.28
## 319  1994-07-01    X5.66  87107.46
## 320  1994-08-01    X5.66  87144.84
## 321  1994-09-01    X5.66  87182.23
## 322  1994-10-01    X5.66  87385.17
## 323  1994-11-01    X5.66  87588.12
## 324  1994-12-01    X5.66  87729.44
## 325  1995-01-01    X5.66  87870.76
## 326  1995-02-01    X5.66  87993.54
## 327  1995-03-01    X5.66  88116.32
## 328  1995-04-01    X5.66  88310.27
## 329  1995-05-01    X5.66  88504.22
## 330  1995-06-01    X5.66  88818.42
## 331  1995-07-01    X5.66  89132.63
## 332  1995-08-01    X5.66  89434.03
## 333  1995-09-01    X5.66  89735.44
## 334  1995-10-01    X5.66  89879.51
## 335  1995-11-01    X5.66  90023.59
## 336  1995-12-01    X5.66  90050.75
## 337  1996-01-01    X5.66  90077.92
## 338  1996-02-01    X5.66  90004.67
## 339  1996-03-01    X5.66  89931.42
## 340  1996-04-01    X5.66  89860.44
## 341  1996-05-01    X5.66  89789.47
## 342  1996-06-01    X5.66  89723.93
## 343  1996-07-01    X5.66  89658.39
## 344  1996-08-01    X5.66  89375.33
## 345  1996-09-01    X5.66  89092.27
## 346  1996-10-01    X5.66  88805.39
## 347  1996-11-01    X5.66  88518.51
## 348  1996-12-01    X5.66  88404.88
## 349  1997-01-01    X5.66  88291.25
## 350  1997-02-01    X5.66  88164.67
## 351  1997-03-01    X5.66  88038.10
## 352  1997-04-01    X5.66  87617.59
## 353  1997-05-01    X5.66  87197.09
## 354  1997-06-01    X5.66  86875.95
## 355  1997-07-01    X5.66  86554.81
## 356  1997-08-01    X5.66  86793.91
## 357  1997-09-01    X5.66  87033.01
## 358  1997-10-01    X5.66  87269.68
## 359  1997-11-01    X5.66  87506.34
## 360  1997-12-01    X5.66  87451.25
## 361  1998-01-01    X5.66  87396.17
## 362  1998-02-01    X5.66  87328.10
## 363  1998-03-01    X5.66  87260.04
## 364  1998-04-01    X5.66  87105.66
## 365  1998-05-01    X5.66  86951.29
## 366  1998-06-01    X5.66  86850.42
## 367  1998-07-01    X5.66  86749.55
## 368  1998-08-01    X5.66  86807.19
## 369  1998-09-01    X5.66  86864.84
## 370  1998-10-01    X5.66  87125.75
## 371  1998-11-01    X5.66  87386.67
## 372  1998-12-01    X5.66  87675.10
## 373  1999-01-01    X5.66  87963.52
## 374  1999-02-01    X5.66  88376.45
## 375  1999-03-01    X5.66  88789.37
## 376  1999-04-01    X5.66  89146.22
## 377  1999-05-01    X5.66  89503.08
## 378  1999-06-01    X5.66  89509.17
## 379  1999-07-01    X5.66  89515.27
## 380  1999-08-01    X5.66  89387.79
## 381  1999-09-01    X5.66  89260.31
## 382  1999-10-01    X5.66  89339.87
## 383  1999-11-01    X5.66  89419.44
## 384  1999-12-01    X5.66  89447.04
## 385  2000-01-01    X5.66  89474.63
## 386  2000-02-01    X5.66  89484.13
## 387  2000-03-01    X5.66  89493.63
## 388  2000-04-01    X5.66  89653.24
## 389  2000-05-01    X5.66  89812.85
## 390  2000-06-01    X5.66  90056.91
## 391  2000-07-01    X5.66  90300.97
## 392  2000-08-01    X5.66  90396.51
## 393  2000-09-01    X5.66  90492.06
## 394  2000-10-01    X5.66  90454.50
## 395  2000-11-01    X5.66  90416.94
## 396  2000-12-01    X5.66  90334.72
## 397  2001-01-01    X5.66  90252.50
## 398  2001-02-01    X5.66  90034.80
## 399  2001-03-01    X5.66  89817.11
## 400  2001-04-01    X5.66  89564.20
## 401  2001-05-01    X5.66  89311.29
## 402  2001-06-01    X5.66  89126.65
## 403  2001-07-01    X5.66  88942.01
## 404  2001-08-01    X5.66  88926.35
## 405  2001-09-01    X5.66  88910.69
## 406  2001-10-01    X5.66  88951.95
## 407  2001-11-01    X5.66  88993.20
## 408  2001-12-01    X5.66  89017.18
## 409  2002-01-01    X5.66  89041.16
## 410  2002-02-01    X5.66  89038.14
## 411  2002-03-01    X5.66  89035.13
## 412  2002-04-01    X5.66  88874.98
## 413  2002-05-01    X5.66  88714.82
## 414  2002-06-01    X5.66  88305.79
## 415  2002-07-01    X5.66  87896.75
## 416  2002-08-01    X5.66  87437.31
## 417  2002-09-01    X5.66  86977.88
## 418  2002-10-01    X5.66  86737.34
## 419  2002-11-01    X5.66  86496.80
## 420  2002-12-01    X5.66  86461.14
## 421  2003-01-01    X5.66  86425.47
## 422  2003-02-01    X5.66  86453.99
## 423  2003-03-01    X5.66  86482.51
## 424  2003-04-01    X5.66  86651.44
## 425  2003-05-01    X5.66  86820.37
## 426  2003-06-01    X5.66  87017.38
## 427  2003-07-01    X5.66  87214.39
## 428  2003-08-01    X5.66  87306.15
## 429  2003-09-01    X5.66  87397.91
## 430  2003-10-01    X5.66  87367.11
## 431  2003-11-01    X5.66  87336.31
## 432  2003-12-01    X5.66  87348.58
## 433  2004-01-01    X5.66  87360.85
## 434  2004-02-01    X5.66  87519.27
## 435  2004-03-01    X5.66  87677.70
## 436  2004-04-01    X5.66  87985.16
## 437  2004-05-01    X5.66  88292.62
## 438  2004-06-01    X5.66  88788.20
## 439  2004-07-01    X5.66  89283.77
## 440  2004-08-01    X5.66  89853.62
## 441  2004-09-01    X5.66  90423.46
## 442  2004-10-01    X5.66  90743.14
## 443  2004-11-01    X5.66  91062.82
## 444  2004-12-01    X5.66  91108.13
## 445  2005-01-01    X5.66  91153.44
## 446  2005-02-01    X5.66  91057.18
## 447  2005-03-01    X5.66  90960.92
## 448  2005-04-01    X5.66  90724.04
## 449  2005-05-01    X5.66  90487.16
## 450  2005-06-01    X5.66  89971.85
## 451  2005-07-01    X5.66  89456.54
## 452  2005-08-01    X5.66  88964.93
## 453  2005-09-01    X5.66  88473.31
## 454  2005-10-01    X5.66  88360.27
## 455  2005-11-01    X5.66  88247.23
## 456  2005-12-01    X5.66  88208.80
## 457  2006-01-01    X5.66  88170.37
## 458  2006-02-01    X5.66  88108.40
## 459  2006-03-01    X5.66  88046.43
## 460  2006-04-01    X5.66  88085.29
## 461  2006-05-01    X5.66  88124.15
## 462  2006-06-01    X5.66  88028.44
## 463  2006-07-01    X5.66  87932.73
## 464  2006-08-01    X5.66  87472.66
## 465  2006-09-01    X5.66  87012.59
## 466  2006-10-01    X5.66  86499.87
## 467  2006-11-01    X5.66  85987.15
## 468  2006-12-01    X5.66  85775.83
## 469  2007-01-01    X5.66  85564.51
## 470  2007-02-01    X5.66  85521.03
## 471  2007-03-01    X5.66  85477.54
## 472  2007-04-01    X5.66  85465.66
## 473  2007-05-01    X5.66  85453.78
## 474  2007-06-01    X5.66  85636.27
## 475  2007-07-01    X5.66  85818.76
## 476  2007-08-01    X5.66  86247.68
## 477  2007-09-01    X5.66  86676.61
## 478  2007-10-01    X5.66  87084.53
## 479  2007-11-01    X5.66  87492.46
## 480  2007-12-01    X5.66  87747.93
## 481  2008-01-01    X5.66  88003.39
## 482  2008-02-01    X5.66  88251.50
## 483  2008-03-01    X5.66  88499.60
## 484  2008-04-01    X5.66  88798.25
## 485  2008-05-01    X5.66  89096.90
## 486  2008-06-01    X5.66  89216.72
## 487  2008-07-01    X5.66  89336.54
## 488  2008-08-01    X5.66  89191.88
## 489  2008-09-01    X5.66  89047.22
## 490  2008-10-01    X5.66  88829.70
## 491  2008-11-01    X5.66  88612.18
## 492  2008-12-01    X5.66  88512.47
## 493  2009-01-01    X5.66  88412.76
## 494  2009-02-01    X5.66  88345.32
## 495  2009-03-01    X5.66  88277.88
## 496  2009-04-01    X5.66  88406.27
## 497  2009-05-01    X5.66  88534.65
## 498  2009-06-01    X5.66  88857.20
## 499  2009-07-01    X5.66  89179.74
## 500  2009-08-01    X5.66  89419.79
## 501  2009-09-01    X5.66  89659.84
## 502  2009-10-01    X5.66  89601.10
## 503  2009-11-01    X5.66  89542.35
## 504  2009-12-01    X5.66  89375.43
## 505  2010-01-01    X5.66  89208.51
## 506  2010-02-01    X5.66  89048.10
## 507  2010-03-01    X5.66  88887.68
## 508  2010-04-01    X5.66  88730.75
## 509  2010-05-01    X5.66  88573.82
## 510  2010-06-01    X5.66  88304.75
## 511  2010-07-01    X5.66  88035.69
## 512  2010-08-01    X5.66  87890.08
## 513  2010-09-01    X5.66  87744.47
## 514  2010-10-01    X5.66  87864.04
## 515  2010-11-01    X5.66  87983.61
## 516  2010-12-01    X5.66  88231.61
## 517  2011-01-01    X5.66  88479.60
## 518  2011-02-01    X5.66  88473.93
## 519  2011-03-01    X5.66  88468.26
## 520  2011-04-01    X5.66  88422.74
## 521  2011-05-01    X5.66  88377.21
## 522  2011-06-01    X5.66  88378.62
## 523  2011-07-01    X5.66  88380.02
## 524  2011-08-01    X5.66  88315.13
## 525  2011-09-01    X5.66  88250.24
## 526  2011-10-01    X5.66  88025.26
## 527  2011-11-01    X5.66  87800.28
## 528  2011-12-01    X5.66  87757.29
## 529  2012-01-01    X5.66  87714.30
## 530  2012-02-01    X5.66  87953.41
## 531  2012-03-01    X5.66  88192.52
## 532  2012-04-01    X5.66  88548.42
## 533  2012-05-01    X5.66  88904.32
## 534  2012-06-01    X5.66  89301.33
## 535  2012-07-01    X5.66  89698.33
## 536  2012-08-01    X5.66  90232.41
## 537  2012-09-01    X5.66  90766.50
## 538  2012-10-01    X5.66  91126.36
## 539  2012-11-01    X5.66  91486.22
## 540  2012-12-01    X5.66  91512.51
## 541  2013-01-01    X5.66  91538.80
## 542  2013-02-01    X5.66  91301.63
## 543  2013-03-01    X5.66  91064.46
## 544  2013-04-01    X5.66  90635.26
## 545  2013-05-01    X5.66  90206.06
## 546  2013-06-01    X5.66  89842.86
## 547  2013-07-01    X5.66  89479.65
## 548  2013-08-01    X5.66  89171.67
## 549  2013-09-01    X5.66  88863.69
## 550  2013-10-01    X5.66  88599.87
## 551  2013-11-01    X5.66  88336.05
## 552  2013-12-01    X5.66  88289.00
## 553  2014-01-01    X5.66  88241.95
## 554  2014-02-01    X5.66  88357.78
## 555  2014-03-01    X5.66  88473.62
## 556  2014-04-01    X5.66  88695.53
## 557  2014-05-01    X5.66  88917.44
## 558  2014-06-01    X5.66  89046.57
## 559  2014-07-01    X5.66  89175.69
## 560  2014-08-01    X5.66  88964.88
## 561  2014-09-01    X5.66  88754.07
## 562  2014-10-01    X5.66  88583.34
## 563  2014-11-01    X5.66  88412.61
## 564  2014-12-01    X5.66  88370.02
## 565  2015-01-01    X5.66  88327.44
## 566  2015-02-01    X5.66  88325.16
## 567  2015-03-01    X5.66  88322.87
## 568  2015-04-01    X5.66  88310.98
## 569  2015-05-01    X5.66  88299.08
## 570  2015-06-01    X5.66  88401.25
## 571  2015-07-01    X5.66  88503.43
## 572  2015-08-01    X5.66  88807.10
## 573  2015-09-01    X5.66  89110.78
## 574  2015-10-01    X5.66  89320.44
## 575  2015-11-01    X5.66  89530.10
## 576  2015-12-01    X5.66  89435.03
## 577  2016-01-01    X5.66  89339.96
## 578  2016-02-01    X5.66  89179.85
## 579  2016-03-01    X5.66  89019.74
## 580  2016-04-01    X5.66  88860.38
## 581  2016-05-01    X5.66  88701.01
## 582  2016-06-01    X5.66  88540.88
## 583  2016-07-01    X5.66  88380.75
## 584  2016-08-01    X5.66  88221.53
## 585  2016-09-01    X5.66  88062.30
## 586  2016-10-01    X5.66  87990.50
## 587  2016-11-01    X5.66  87918.69
## 588  2016-12-01    X5.66  87945.46
## 589  2017-01-01    X5.66  87972.22
## 590  2017-02-01    X5.66  87917.27
## 591  2017-03-01    X5.66  87862.31
## 592  2017-04-01    X5.66  87692.90
## 593  2017-05-01    X5.66  87523.48
## 594  2017-06-01    X5.66  87357.82
## 595  2017-07-01    X5.66  87192.17
## 596  2017-08-01    X5.66  87011.17
## 597  2017-09-01    X5.66  86830.16
## 598  2017-10-01    X5.66  86627.58
## 599  2017-11-01    X5.66  86424.99
## 600  2017-12-01    X5.66  86207.49
## 601  1993-01-01    X6.17 102388.62
## 602  1993-02-01    X6.17 102499.50
## 603  1993-03-01    X6.17 102610.39
## 604  1993-04-01    X6.17 102702.91
## 605  1993-05-01    X6.17 102795.43
## 606  1993-06-01    X6.17 102882.05
## 607  1993-07-01    X6.17 102968.66
## 608  1993-08-01    X6.17 103045.11
## 609  1993-09-01    X6.17 103121.55
## 610  1993-10-01    X6.17 103021.81
## 611  1993-11-01    X6.17 102922.07
## 612  1993-12-01    X6.17 102691.69
## 613  1994-01-01    X6.17 102461.30
## 614  1994-02-01    X6.17 102264.64
## 615  1994-03-01    X6.17 102067.99
## 616  1994-04-01    X6.17 101786.09
## 617  1994-05-01    X6.17 101504.19
## 618  1994-06-01    X6.17 101269.01
## 619  1994-07-01    X6.17 101033.83
## 620  1994-08-01    X6.17 101015.65
## 621  1994-09-01    X6.17 100997.47
## 622  1994-10-01    X6.17 101169.20
## 623  1994-11-01    X6.17 101340.93
## 624  1994-12-01    X6.17 101465.75
## 625  1995-01-01    X6.17 101590.57
## 626  1995-02-01    X6.17 101717.27
## 627  1995-03-01    X6.17 101843.97
## 628  1995-04-01    X6.17 102042.63
## 629  1995-05-01    X6.17 102241.29
## 630  1995-06-01    X6.17 102510.01
## 631  1995-07-01    X6.17 102778.72
## 632  1995-08-01    X6.17 103034.20
## 633  1995-09-01    X6.17 103289.67
## 634  1995-10-01    X6.17 103415.14
## 635  1995-11-01    X6.17 103540.60
## 636  1995-12-01    X6.17 103557.90
## 637  1996-01-01    X6.17 103575.20
## 638  1996-02-01    X6.17 103500.18
## 639  1996-03-01    X6.17 103425.16
## 640  1996-04-01    X6.17 103367.69
## 641  1996-05-01    X6.17 103310.23
## 642  1996-06-01    X6.17 103270.65
## 643  1996-07-01    X6.17 103231.08
## 644  1996-08-01    X6.17 102940.47
## 645  1996-09-01    X6.17 102649.86
## 646  1996-10-01    X6.17 102312.49
## 647  1996-11-01    X6.17 101975.13
## 648  1996-12-01    X6.17 101826.53
## 649  1997-01-01    X6.17 101677.93
## 650  1997-02-01    X6.17 101543.55
## 651  1997-03-01    X6.17 101409.18
## 652  1997-04-01    X6.17 101034.13
## 653  1997-05-01    X6.17 100659.08
## 654  1997-06-01    X6.17 100432.44
## 655  1997-07-01    X6.17 100205.79
## 656  1997-08-01    X6.17 100512.84
## 657  1997-09-01    X6.17 100819.88
## 658  1997-10-01    X6.17 101072.88
## 659  1997-11-01    X6.17 101325.88
## 660  1997-12-01    X6.17 101274.76
## 661  1998-01-01    X6.17 101223.63
## 662  1998-02-01    X6.17 101161.04
## 663  1998-03-01    X6.17 101098.45
## 664  1998-04-01    X6.17 100913.15
## 665  1998-05-01    X6.17 100727.85
## 666  1998-06-01    X6.17 100560.85
## 667  1998-07-01    X6.17 100393.85
## 668  1998-08-01    X6.17 100409.69
## 669  1998-09-01    X6.17 100425.52
## 670  1998-10-01    X6.17 100662.44
## 671  1998-11-01    X6.17 100899.35
## 672  1998-12-01    X6.17 101173.59
## 673  1999-01-01    X6.17 101447.83
## 674  1999-02-01    X6.17 101881.75
## 675  1999-03-01    X6.17 102315.66
## 676  1999-04-01    X6.17 102711.49
## 677  1999-05-01    X6.17 103107.32
## 678  1999-06-01    X6.17 103158.10
## 679  1999-07-01    X6.17 103208.89
## 680  1999-08-01    X6.17 103120.09
## 681  1999-09-01    X6.17 103031.29
## 682  1999-10-01    X6.17 103125.04
## 683  1999-11-01    X6.17 103218.78
## 684  1999-12-01    X6.17 103216.75
## 685  2000-01-01    X6.17 103214.73
## 686  2000-02-01    X6.17 103188.37
## 687  2000-03-01    X6.17 103162.01
## 688  2000-04-01    X6.17 103298.47
## 689  2000-05-01    X6.17 103434.93
## 690  2000-06-01    X6.17 103636.73
## 691  2000-07-01    X6.17 103838.54
## 692  2000-08-01    X6.17 103880.80
## 693  2000-09-01    X6.17 103923.05
## 694  2000-10-01    X6.17 103869.76
## 695  2000-11-01    X6.17 103816.47
## 696  2000-12-01    X6.17 103746.69
## 697  2001-01-01    X6.17 103676.91
## 698  2001-02-01    X6.17 103480.90
## 699  2001-03-01    X6.17 103284.90
## 700  2001-04-01    X6.17 103081.59
## 701  2001-05-01    X6.17 102878.28
## 702  2001-06-01    X6.17 102765.92
## 703  2001-07-01    X6.17 102653.57
## 704  2001-08-01    X6.17 102686.87
## 705  2001-09-01    X6.17 102720.17
## 706  2001-10-01    X6.17 102775.25
## 707  2001-11-01    X6.17 102830.33
## 708  2001-12-01    X6.17 102856.41
## 709  2002-01-01    X6.17 102882.49
## 710  2002-02-01    X6.17 102874.16
## 711  2002-03-01    X6.17 102865.84
## 712  2002-04-01    X6.17 102717.72
## 713  2002-05-01    X6.17 102569.59
## 714  2002-06-01    X6.17 102188.63
## 715  2002-07-01    X6.17 101807.67
## 716  2002-08-01    X6.17 101366.86
## 717  2002-09-01    X6.17 100926.05
## 718  2002-10-01    X6.17 100694.22
## 719  2002-11-01    X6.17 100462.40
## 720  2002-12-01    X6.17 100420.89
## 721  2003-01-01    X6.17 100379.37
## 722  2003-02-01    X6.17 100383.17
## 723  2003-03-01    X6.17 100386.97
## 724  2003-04-01    X6.17 100511.12
## 725  2003-05-01    X6.17 100635.28
## 726  2003-06-01    X6.17 100765.82
## 727  2003-07-01    X6.17 100896.36
## 728  2003-08-01    X6.17 100922.66
## 729  2003-09-01    X6.17 100948.96
## 730  2003-10-01    X6.17 100887.75
## 731  2003-11-01    X6.17 100826.54
## 732  2003-12-01    X6.17 100826.92
## 733  2004-01-01    X6.17 100827.29
## 734  2004-02-01    X6.17 100984.02
## 735  2004-03-01    X6.17 101140.75
## 736  2004-04-01    X6.17 101464.16
## 737  2004-05-01    X6.17 101787.56
## 738  2004-06-01    X6.17 102299.28
## 739  2004-07-01    X6.17 102810.99
## 740  2004-08-01    X6.17 103395.13
## 741  2004-09-01    X6.17 103979.27
## 742  2004-10-01    X6.17 104297.78
## 743  2004-11-01    X6.17 104616.30
## 744  2004-12-01    X6.17 104668.31
## 745  2005-01-01    X6.17 104720.32
## 746  2005-02-01    X6.17 104627.90
## 747  2005-03-01    X6.17 104535.48
## 748  2005-04-01    X6.17 104292.49
## 749  2005-05-01    X6.17 104049.51
## 750  2005-06-01    X6.17 103541.58
## 751  2005-07-01    X6.17 103033.64
## 752  2005-08-01    X6.17 102558.41
## 753  2005-09-01    X6.17 102083.17
## 754  2005-10-01    X6.17 101982.45
## 755  2005-11-01    X6.17 101881.73
## 756  2005-12-01    X6.17 101855.13
## 757  2006-01-01    X6.17 101828.52
## 758  2006-02-01    X6.17 101803.52
## 759  2006-03-01    X6.17 101778.53
## 760  2006-04-01    X6.17 101892.49
## 761  2006-05-01    X6.17 102006.45
## 762  2006-06-01    X6.17 101968.31
## 763  2006-07-01    X6.17 101930.18
## 764  2006-08-01    X6.17 101467.53
## 765  2006-09-01    X6.17 101004.89
## 766  2006-10-01    X6.17 100479.49
## 767  2006-11-01    X6.17  99954.10
## 768  2006-12-01    X6.17  99722.92
## 769  2007-01-01    X6.17  99491.74
## 770  2007-02-01    X6.17  99404.88
## 771  2007-03-01    X6.17  99318.03
## 772  2007-04-01    X6.17  99267.40
## 773  2007-05-01    X6.17  99216.77
## 774  2007-06-01    X6.17  99381.84
## 775  2007-07-01    X6.17  99546.91
## 776  2007-08-01    X6.17  99986.53
## 777  2007-09-01    X6.17 100426.14
## 778  2007-10-01    X6.17 100839.02
## 779  2007-11-01    X6.17 101251.90
## 780  2007-12-01    X6.17 101515.97
## 781  2008-01-01    X6.17 101780.04
## 782  2008-02-01    X6.17 102037.04
## 783  2008-03-01    X6.17 102294.04
## 784  2008-04-01    X6.17 102579.61
## 785  2008-05-01    X6.17 102865.18
## 786  2008-06-01    X6.17 102988.74
## 787  2008-07-01    X6.17 103112.31
## 788  2008-08-01    X6.17 102981.83
## 789  2008-09-01    X6.17 102851.36
## 790  2008-10-01    X6.17 102618.27
## 791  2008-11-01    X6.17 102385.18
## 792  2008-12-01    X6.17 102264.92
## 793  2009-01-01    X6.17 102144.66
## 794  2009-02-01    X6.17 102065.67
## 795  2009-03-01    X6.17 101986.69
## 796  2009-04-01    X6.17 102143.06
## 797  2009-05-01    X6.17 102299.42
## 798  2009-06-01    X6.17 102652.39
## 799  2009-07-01    X6.17 103005.36
## 800  2009-08-01    X6.17 103267.80
## 801  2009-09-01    X6.17 103530.24
## 802  2009-10-01    X6.17 103507.64
## 803  2009-11-01    X6.17 103485.04
## 804  2009-12-01    X6.17 103342.16
## 805  2010-01-01    X6.17 103199.28
## 806  2010-02-01    X6.17 103021.29
## 807  2010-03-01    X6.17 102843.30
## 808  2010-04-01    X6.17 102657.92
## 809  2010-05-01    X6.17 102472.55
## 810  2010-06-01    X6.17 102194.48
## 811  2010-07-01    X6.17 101916.41
## 812  2010-08-01    X6.17 101761.87
## 813  2010-09-01    X6.17 101607.32
## 814  2010-10-01    X6.17 101711.48
## 815  2010-11-01    X6.17 101815.64
## 816  2010-12-01    X6.17 102058.21
## 817  2011-01-01    X6.17 102300.78
## 818  2011-02-01    X6.17 102292.24
## 819  2011-03-01    X6.17 102283.69
## 820  2011-04-01    X6.17 102198.60
## 821  2011-05-01    X6.17 102113.50
## 822  2011-06-01    X6.17 102066.22
## 823  2011-07-01    X6.17 102018.94
## 824  2011-08-01    X6.17 101956.11
## 825  2011-09-01    X6.17 101893.29
## 826  2011-10-01    X6.17 101688.81
## 827  2011-11-01    X6.17 101484.34
## 828  2011-12-01    X6.17 101452.70
## 829  2012-01-01    X6.17 101421.05
## 830  2012-02-01    X6.17 101673.60
## 831  2012-03-01    X6.17 101926.15
## 832  2012-04-01    X6.17 102291.42
## 833  2012-05-01    X6.17 102656.68
## 834  2012-06-01    X6.17 103032.24
## 835  2012-07-01    X6.17 103407.80
## 836  2012-08-01    X6.17 103930.58
## 837  2012-09-01    X6.17 104453.36
## 838  2012-10-01    X6.17 104809.29
## 839  2012-11-01    X6.17 105165.22
## 840  2012-12-01    X6.17 105191.18
## 841  2013-01-01    X6.17 105217.13
## 842  2013-02-01    X6.17 104981.95
## 843  2013-03-01    X6.17 104746.77
## 844  2013-04-01    X6.17 104344.57
## 845  2013-05-01    X6.17 103942.37
## 846  2013-06-01    X6.17 103659.77
## 847  2013-07-01    X6.17 103377.18
## 848  2013-08-01    X6.17 103138.64
## 849  2013-09-01    X6.17 102900.11
## 850  2013-10-01    X6.17 102668.22
## 851  2013-11-01    X6.17 102436.33
## 852  2013-12-01    X6.17 102406.27
## 853  2014-01-01    X6.17 102376.21
## 854  2014-02-01    X6.17 102497.76
## 855  2014-03-01    X6.17 102619.31
## 856  2014-04-01    X6.17 102806.89
## 857  2014-05-01    X6.17 102994.46
## 858  2014-06-01    X6.17 103051.75
## 859  2014-07-01    X6.17 103109.04
## 860  2014-08-01    X6.17 102887.13
## 861  2014-09-01    X6.17 102665.22
## 862  2014-10-01    X6.17 102546.15
## 863  2014-11-01    X6.17 102427.07
## 864  2014-12-01    X6.17 102402.16
## 865  2015-01-01    X6.17 102377.24
## 866  2015-02-01    X6.17 102357.41
## 867  2015-03-01    X6.17 102337.58
## 868  2015-04-01    X6.17 102328.67
## 869  2015-05-01    X6.17 102319.77
## 870  2015-06-01    X6.17 102434.23
## 871  2015-07-01    X6.17 102548.69
## 872  2015-08-01    X6.17 102843.49
## 873  2015-09-01    X6.17 103138.29
## 874  2015-10-01    X6.17 103362.28
## 875  2015-11-01    X6.17 103586.27
## 876  2015-12-01    X6.17 103540.38
## 877  2016-01-01    X6.17 103494.48
## 878  2016-02-01    X6.17 103352.13
## 879  2016-03-01    X6.17 103209.78
## 880  2016-04-01    X6.17 102980.32
## 881  2016-05-01    X6.17 102750.85
## 882  2016-06-01    X6.17 102514.33
## 883  2016-07-01    X6.17 102277.80
## 884  2016-08-01    X6.17 102103.74
## 885  2016-09-01    X6.17 101929.67
## 886  2016-10-01    X6.17 101855.94
## 887  2016-11-01    X6.17 101782.21
## 888  2016-12-01    X6.17 101791.71
## 889  2017-01-01    X6.17 101801.21
## 890  2017-02-01    X6.17 101751.30
## 891  2017-03-01    X6.17 101701.40
## 892  2017-04-01    X6.17 101510.48
## 893  2017-05-01    X6.17 101319.56
## 894  2017-06-01    X6.17 101122.06
## 895  2017-07-01    X6.17 100924.55
## 896  2017-08-01    X6.17 100700.56
## 897  2017-09-01    X6.17 100476.58
## 898  2017-10-01    X6.17 100223.49
## 899  2017-11-01    X6.17  99970.39
## 900  2017-12-01    X6.17  99698.47
## 901  1993-01-01    X6.69 118223.57
## 902  1993-02-01    X6.69 118350.04
## 903  1993-03-01    X6.69 118476.51
## 904  1993-04-01    X6.69 118578.98
## 905  1993-05-01    X6.69 118681.46
## 906  1993-06-01    X6.69 118776.39
## 907  1993-07-01    X6.69 118871.31
## 908  1993-08-01    X6.69 118963.18
## 909  1993-09-01    X6.69 119055.05
## 910  1993-10-01    X6.69 118971.90
## 911  1993-11-01    X6.69 118888.75
## 912  1993-12-01    X6.69 118650.74
## 913  1994-01-01    X6.69 118412.74
## 914  1994-02-01    X6.69 118201.22
## 915  1994-03-01    X6.69 117989.70
## 916  1994-04-01    X6.69 117718.64
## 917  1994-05-01    X6.69 117447.59
## 918  1994-06-01    X6.69 117278.22
## 919  1994-07-01    X6.69 117108.85
## 920  1994-08-01    X6.69 117189.60
## 921  1994-09-01    X6.69 117270.35
## 922  1994-10-01    X6.69 117510.46
## 923  1994-11-01    X6.69 117750.56
## 924  1994-12-01    X6.69 117910.18
## 925  1995-01-01    X6.69 118069.80
## 926  1995-02-01    X6.69 118180.89
## 927  1995-03-01    X6.69 118291.98
## 928  1995-04-01    X6.69 118420.35
## 929  1995-05-01    X6.69 118548.72
## 930  1995-06-01    X6.69 118717.30
## 931  1995-07-01    X6.69 118885.89
## 932  1995-08-01    X6.69 119036.89
## 933  1995-09-01    X6.69 119187.89
## 934  1995-10-01    X6.69 119257.57
## 935  1995-11-01    X6.69 119327.24
## 936  1995-12-01    X6.69 119349.71
## 937  1996-01-01    X6.69 119372.17
## 938  1996-02-01    X6.69 119322.09
## 939  1996-03-01    X6.69 119272.01
## 940  1996-04-01    X6.69 119263.00
## 941  1996-05-01    X6.69 119253.99
## 942  1996-06-01    X6.69 119279.19
## 943  1996-07-01    X6.69 119304.39
## 944  1996-08-01    X6.69 119058.83
## 945  1996-09-01    X6.69 118813.26
## 946  1996-10-01    X6.69 118503.88
## 947  1996-11-01    X6.69 118194.51
## 948  1996-12-01    X6.69 118062.52
## 949  1997-01-01    X6.69 117930.53
## 950  1997-02-01    X6.69 117804.69
## 951  1997-03-01    X6.69 117678.85
## 952  1997-04-01    X6.69 117281.78
## 953  1997-05-01    X6.69 116884.72
## 954  1997-06-01    X6.69 116614.80
## 955  1997-07-01    X6.69 116344.89
## 956  1997-08-01    X6.69 116621.25
## 957  1997-09-01    X6.69 116897.62
## 958  1997-10-01    X6.69 117127.18
## 959  1997-11-01    X6.69 117356.73
## 960  1997-12-01    X6.69 117277.99
## 961  1998-01-01    X6.69 117199.24
## 962  1998-02-01    X6.69 117084.64
## 963  1998-03-01    X6.69 116970.05
## 964  1998-04-01    X6.69 116736.81
## 965  1998-05-01    X6.69 116503.57
## 966  1998-06-01    X6.69 116350.99
## 967  1998-07-01    X6.69 116198.41
## 968  1998-08-01    X6.69 116254.48
## 969  1998-09-01    X6.69 116310.56
## 970  1998-10-01    X6.69 116569.26
## 971  1998-11-01    X6.69 116827.97
## 972  1998-12-01    X6.69 117119.00
## 973  1999-01-01    X6.69 117410.04
## 974  1999-02-01    X6.69 117847.46
## 975  1999-03-01    X6.69 118284.87
## 976  1999-04-01    X6.69 118651.92
## 977  1999-05-01    X6.69 119018.97
## 978  1999-06-01    X6.69 119003.76
## 979  1999-07-01    X6.69 118988.55
## 980  1999-08-01    X6.69 118835.11
## 981  1999-09-01    X6.69 118681.67
## 982  1999-10-01    X6.69 118752.32
## 983  1999-11-01    X6.69 118822.96
## 984  1999-12-01    X6.69 118832.11
## 985  2000-01-01    X6.69 118841.26
## 986  2000-02-01    X6.69 118833.18
## 987  2000-03-01    X6.69 118825.10
## 988  2000-04-01    X6.69 119015.59
## 989  2000-05-01    X6.69 119206.08
## 990  2000-06-01    X6.69 119526.58
## 991  2000-07-01    X6.69 119847.07
## 992  2000-08-01    X6.69 120000.30
## 993  2000-09-01    X6.69 120153.54
## 994  2000-10-01    X6.69 120147.22
## 995  2000-11-01    X6.69 120140.89
## 996  2000-12-01    X6.69 120084.80
## 997  2001-01-01    X6.69 120028.71
## 998  2001-02-01    X6.69 119811.08
## 999  2001-03-01    X6.69 119593.45
## 1000 2001-04-01    X6.69 119292.92
## 1001 2001-05-01    X6.69 118992.39
## 1002 2001-06-01    X6.69 118719.17
## 1003 2001-07-01    X6.69 118445.94
## 1004 2001-08-01    X6.69 118365.86
## 1005 2001-09-01    X6.69 118285.78
## 1006 2001-10-01    X6.69 118308.30
## 1007 2001-11-01    X6.69 118330.83
## 1008 2001-12-01    X6.69 118369.14
## 1009 2002-01-01    X6.69 118407.46
## 1010 2002-02-01    X6.69 118439.88
## 1011 2002-03-01    X6.69 118472.30
## 1012 2002-04-01    X6.69 118395.21
## 1013 2002-05-01    X6.69 118318.12
## 1014 2002-06-01    X6.69 118013.31
## 1015 2002-07-01    X6.69 117708.51
## 1016 2002-08-01    X6.69 117308.62
## 1017 2002-09-01    X6.69 116908.73
## 1018 2002-10-01    X6.69 116666.55
## 1019 2002-11-01    X6.69 116424.37
## 1020 2002-12-01    X6.69 116374.28
## 1021 2003-01-01    X6.69 116324.20
## 1022 2003-02-01    X6.69 116326.20
## 1023 2003-03-01    X6.69 116328.19
## 1024 2003-04-01    X6.69 116439.51
## 1025 2003-05-01    X6.69 116550.83
## 1026 2003-06-01    X6.69 116672.71
## 1027 2003-07-01    X6.69 116794.60
## 1028 2003-08-01    X6.69 116824.64
## 1029 2003-09-01    X6.69 116854.69
## 1030 2003-10-01    X6.69 116792.16
## 1031 2003-11-01    X6.69 116729.63
## 1032 2003-12-01    X6.69 116727.50
## 1033 2004-01-01    X6.69 116725.38
## 1034 2004-02-01    X6.69 116882.01
## 1035 2004-03-01    X6.69 117038.65
## 1036 2004-04-01    X6.69 117354.57
## 1037 2004-05-01    X6.69 117670.50
## 1038 2004-06-01    X6.69 118186.39
## 1039 2004-07-01    X6.69 118702.29
## 1040 2004-08-01    X6.69 119285.45
## 1041 2004-09-01    X6.69 119868.61
## 1042 2004-10-01    X6.69 120180.79
## 1043 2004-11-01    X6.69 120492.98
## 1044 2004-12-01    X6.69 120532.70
## 1045 2005-01-01    X6.69 120572.42
## 1046 2005-02-01    X6.69 120514.33
## 1047 2005-03-01    X6.69 120456.25
## 1048 2005-04-01    X6.69 120306.99
## 1049 2005-05-01    X6.69 120157.74
## 1050 2005-06-01    X6.69 119681.73
## 1051 2005-07-01    X6.69 119205.71
## 1052 2005-08-01    X6.69 118702.40
## 1053 2005-09-01    X6.69 118199.08
## 1054 2005-10-01    X6.69 118060.16
## 1055 2005-11-01    X6.69 117921.23
## 1056 2005-12-01    X6.69 117854.13
## 1057 2006-01-01    X6.69 117787.02
## 1058 2006-02-01    X6.69 117679.79
## 1059 2006-03-01    X6.69 117572.56
## 1060 2006-04-01    X6.69 117579.72
## 1061 2006-05-01    X6.69 117586.89
## 1062 2006-06-01    X6.69 117527.74
## 1063 2006-07-01    X6.69 117468.60
## 1064 2006-08-01    X6.69 117029.06
## 1065 2006-09-01    X6.69 116589.52
## 1066 2006-10-01    X6.69 116085.33
## 1067 2006-11-01    X6.69 115581.15
## 1068 2006-12-01    X6.69 115369.71
## 1069 2007-01-01    X6.69 115158.27
## 1070 2007-02-01    X6.69 115098.35
## 1071 2007-03-01    X6.69 115038.43
## 1072 2007-04-01    X6.69 115022.01
## 1073 2007-05-01    X6.69 115005.58
## 1074 2007-06-01    X6.69 115217.01
## 1075 2007-07-01    X6.69 115428.43
## 1076 2007-08-01    X6.69 115928.89
## 1077 2007-09-01    X6.69 116429.34
## 1078 2007-10-01    X6.69 116887.13
## 1079 2007-11-01    X6.69 117344.91
## 1080 2007-12-01    X6.69 117630.30
## 1081 2008-01-01    X6.69 117915.68
## 1082 2008-02-01    X6.69 118198.32
## 1083 2008-03-01    X6.69 118480.96
## 1084 2008-04-01    X6.69 118780.70
## 1085 2008-05-01    X6.69 119080.44
## 1086 2008-06-01    X6.69 119167.51
## 1087 2008-07-01    X6.69 119254.58
## 1088 2008-08-01    X6.69 119080.87
## 1089 2008-09-01    X6.69 118907.16
## 1090 2008-10-01    X6.69 118659.52
## 1091 2008-11-01    X6.69 118411.89
## 1092 2008-12-01    X6.69 118298.06
## 1093 2009-01-01    X6.69 118184.23
## 1094 2009-02-01    X6.69 118096.43
## 1095 2009-03-01    X6.69 118008.63
## 1096 2009-04-01    X6.69 118136.09
## 1097 2009-05-01    X6.69 118263.54
## 1098 2009-06-01    X6.69 118585.93
## 1099 2009-07-01    X6.69 118908.32
## 1100 2009-08-01    X6.69 119165.76
## 1101 2009-09-01    X6.69 119423.20
## 1102 2009-10-01    X6.69 119385.39
## 1103 2009-11-01    X6.69 119347.58
## 1104 2009-12-01    X6.69 119188.56
## 1105 2010-01-01    X6.69 119029.54
## 1106 2010-02-01    X6.69 118870.69
## 1107 2010-03-01    X6.69 118711.83
## 1108 2010-04-01    X6.69 118556.75
## 1109 2010-05-01    X6.69 118401.66
## 1110 2010-06-01    X6.69 118130.57
## 1111 2010-07-01    X6.69 117859.49
## 1112 2010-08-01    X6.69 117682.70
## 1113 2010-09-01    X6.69 117505.92
## 1114 2010-10-01    X6.69 117584.43
## 1115 2010-11-01    X6.69 117662.95
## 1116 2010-12-01    X6.69 117879.18
## 1117 2011-01-01    X6.69 118095.40
## 1118 2011-02-01    X6.69 118074.22
## 1119 2011-03-01    X6.69 118053.03
## 1120 2011-04-01    X6.69 117965.61
## 1121 2011-05-01    X6.69 117878.19
## 1122 2011-06-01    X6.69 117818.06
## 1123 2011-07-01    X6.69 117757.93
## 1124 2011-08-01    X6.69 117698.35
## 1125 2011-09-01    X6.69 117638.77
## 1126 2011-10-01    X6.69 117469.77
## 1127 2011-11-01    X6.69 117300.76
## 1128 2011-12-01    X6.69 117288.30
## 1129 2012-01-01    X6.69 117275.84
## 1130 2012-02-01    X6.69 117532.21
## 1131 2012-03-01    X6.69 117788.58
## 1132 2012-04-01    X6.69 118179.74
## 1133 2012-05-01    X6.69 118570.89
## 1134 2012-06-01    X6.69 118996.08
## 1135 2012-07-01    X6.69 119421.26
## 1136 2012-08-01    X6.69 119992.77
## 1137 2012-09-01    X6.69 120564.28
## 1138 2012-10-01    X6.69 120947.60
## 1139 2012-11-01    X6.69 121330.93
## 1140 2012-12-01    X6.69 121363.91
## 1141 2013-01-01    X6.69 121396.88
## 1142 2013-02-01    X6.69 121155.07
## 1143 2013-03-01    X6.69 120913.26
## 1144 2013-04-01    X6.69 120481.95
## 1145 2013-05-01    X6.69 120050.65
## 1146 2013-06-01    X6.69 119698.74
## 1147 2013-07-01    X6.69 119346.84
## 1148 2013-08-01    X6.69 119033.57
## 1149 2013-09-01    X6.69 118720.31
## 1150 2013-10-01    X6.69 118449.13
## 1151 2013-11-01    X6.69 118177.95
## 1152 2013-12-01    X6.69 118140.30
## 1153 2014-01-01    X6.69 118102.64
## 1154 2014-02-01    X6.69 118220.76
## 1155 2014-03-01    X6.69 118338.88
## 1156 2014-04-01    X6.69 118529.46
## 1157 2014-05-01    X6.69 118720.04
## 1158 2014-06-01    X6.69 118802.45
## 1159 2014-07-01    X6.69 118884.85
## 1160 2014-08-01    X6.69 118679.50
## 1161 2014-09-01    X6.69 118474.15
## 1162 2014-10-01    X6.69 118361.11
## 1163 2014-11-01    X6.69 118248.08
## 1164 2014-12-01    X6.69 118245.06
## 1165 2015-01-01    X6.69 118242.05
## 1166 2015-02-01    X6.69 118244.33
## 1167 2015-03-01    X6.69 118246.60
## 1168 2015-04-01    X6.69 118240.44
## 1169 2015-05-01    X6.69 118234.27
## 1170 2015-06-01    X6.69 118337.65
## 1171 2015-07-01    X6.69 118441.03
## 1172 2015-08-01    X6.69 118727.40
## 1173 2015-09-01    X6.69 119013.78
## 1174 2015-10-01    X6.69 119223.28
## 1175 2015-11-01    X6.69 119432.78
## 1176 2015-12-01    X6.69 119370.64
## 1177 2016-01-01    X6.69 119308.51
## 1178 2016-02-01    X6.69 119206.77
## 1179 2016-03-01    X6.69 119105.04
## 1180 2016-04-01    X6.69 118951.86
## 1181 2016-05-01    X6.69 118798.68
## 1182 2016-06-01    X6.69 118603.97
## 1183 2016-07-01    X6.69 118409.26
## 1184 2016-08-01    X6.69 118251.57
## 1185 2016-09-01    X6.69 118093.88
## 1186 2016-10-01    X6.69 118018.68
## 1187 2016-11-01    X6.69 117943.49
## 1188 2016-12-01    X6.69 117929.42
## 1189 2017-01-01    X6.69 117915.35
## 1190 2017-02-01    X6.69 117849.22
## 1191 2017-03-01    X6.69 117783.10
## 1192 2017-04-01    X6.69 117588.19
## 1193 2017-05-01    X6.69 117393.28
## 1194 2017-06-01    X6.69 117160.50
## 1195 2017-07-01    X6.69 116927.72
## 1196 2017-08-01    X6.69 116674.97
## 1197 2017-09-01    X6.69 116422.23
## 1198 2017-10-01    X6.69 116147.27
## 1199 2017-11-01    X6.69 115872.31
## 1200 2017-12-01    X6.69 115577.37
## 1201 1993-01-01     X7.2 137939.62
## 1202 1993-02-01     X7.2 138095.47
## 1203 1993-03-01     X7.2 138251.33
## 1204 1993-04-01     X7.2 138378.21
## 1205 1993-05-01     X7.2 138505.10
## 1206 1993-06-01     X7.2 138622.46
## 1207 1993-07-01     X7.2 138739.81
## 1208 1993-08-01     X7.2 138852.56
## 1209 1993-09-01     X7.2 138965.30
## 1210 1993-10-01     X7.2 138872.59
## 1211 1993-11-01     X7.2 138779.89
## 1212 1993-12-01     X7.2 138519.61
## 1213 1994-01-01     X7.2 138259.33
## 1214 1994-02-01     X7.2 138027.73
## 1215 1994-03-01     X7.2 137796.12
## 1216 1994-04-01     X7.2 137508.17
## 1217 1994-05-01     X7.2 137220.22
## 1218 1994-06-01     X7.2 137003.87
## 1219 1994-07-01     X7.2 136787.53
## 1220 1994-08-01     X7.2 136799.86
## 1221 1994-09-01     X7.2 136812.19
## 1222 1994-10-01     X7.2 137027.98
## 1223 1994-11-01     X7.2 137243.78
## 1224 1994-12-01     X7.2 137396.43
## 1225 1995-01-01     X7.2 137549.09
## 1226 1995-02-01     X7.2 137665.79
## 1227 1995-03-01     X7.2 137782.48
## 1228 1995-04-01     X7.2 137943.66
## 1229 1995-05-01     X7.2 138104.84
## 1230 1995-06-01     X7.2 138446.80
## 1231 1995-07-01     X7.2 138788.75
## 1232 1995-08-01     X7.2 139186.86
## 1233 1995-09-01     X7.2 139584.96
## 1234 1995-10-01     X7.2 139787.99
## 1235 1995-11-01     X7.2 139991.02
## 1236 1995-12-01     X7.2 140049.70
## 1237 1996-01-01     X7.2 140108.39
## 1238 1996-02-01     X7.2 140057.46
## 1239 1996-03-01     X7.2 140006.53
## 1240 1996-04-01     X7.2 139901.88
## 1241 1996-05-01     X7.2 139797.22
## 1242 1996-06-01     X7.2 139597.59
## 1243 1996-07-01     X7.2 139397.96
## 1244 1996-08-01     X7.2 138962.05
## 1245 1996-09-01     X7.2 138526.15
## 1246 1996-10-01     X7.2 138184.24
## 1247 1996-11-01     X7.2 137842.33
## 1248 1996-12-01     X7.2 137721.46
## 1249 1997-01-01     X7.2 137600.60
## 1250 1997-02-01     X7.2 137495.09
## 1251 1997-03-01     X7.2 137389.58
## 1252 1997-04-01     X7.2 137033.35
## 1253 1997-05-01     X7.2 136677.11
## 1254 1997-06-01     X7.2 136437.30
## 1255 1997-07-01     X7.2 136197.48
## 1256 1997-08-01     X7.2 136467.37
## 1257 1997-09-01     X7.2 136737.26
## 1258 1997-10-01     X7.2 136946.98
## 1259 1997-11-01     X7.2 137156.70
## 1260 1997-12-01     X7.2 137069.74
## 1261 1998-01-01     X7.2 136982.77
## 1262 1998-02-01     X7.2 136877.78
## 1263 1998-03-01     X7.2 136772.79
## 1264 1998-04-01     X7.2 136574.33
## 1265 1998-05-01     X7.2 136375.86
## 1266 1998-06-01     X7.2 136308.52
## 1267 1998-07-01     X7.2 136241.18
## 1268 1998-08-01     X7.2 136386.59
## 1269 1998-09-01     X7.2 136532.00
## 1270 1998-10-01     X7.2 136847.02
## 1271 1998-11-01     X7.2 137162.04
## 1272 1998-12-01     X7.2 137473.43
## 1273 1999-01-01     X7.2 137784.82
## 1274 1999-02-01     X7.2 138229.07
## 1275 1999-03-01     X7.2 138673.32
## 1276 1999-04-01     X7.2 139037.61
## 1277 1999-05-01     X7.2 139401.90
## 1278 1999-06-01     X7.2 139319.22
## 1279 1999-07-01     X7.2 139236.54
## 1280 1999-08-01     X7.2 138995.38
## 1281 1999-09-01     X7.2 138754.23
## 1282 1999-10-01     X7.2 138775.66
## 1283 1999-11-01     X7.2 138797.09
## 1284 1999-12-01     X7.2 138783.91
## 1285 2000-01-01     X7.2 138770.74
## 1286 2000-02-01     X7.2 138769.64
## 1287 2000-03-01     X7.2 138768.54
## 1288 2000-04-01     X7.2 138989.45
## 1289 2000-05-01     X7.2 139210.37
## 1290 2000-06-01     X7.2 139609.70
## 1291 2000-07-01     X7.2 140009.03
## 1292 2000-08-01     X7.2 140266.42
## 1293 2000-09-01     X7.2 140523.82
## 1294 2000-10-01     X7.2 140568.48
## 1295 2000-11-01     X7.2 140613.15
## 1296 2000-12-01     X7.2 140546.04
## 1297 2001-01-01     X7.2 140478.94
## 1298 2001-02-01     X7.2 140209.53
## 1299 2001-03-01     X7.2 139940.12
## 1300 2001-04-01     X7.2 139582.66
## 1301 2001-05-01     X7.2 139225.19
## 1302 2001-06-01     X7.2 138956.00
## 1303 2001-07-01     X7.2 138686.82
## 1304 2001-08-01     X7.2 138637.72
## 1305 2001-09-01     X7.2 138588.63
## 1306 2001-10-01     X7.2 138631.80
## 1307 2001-11-01     X7.2 138674.98
## 1308 2001-12-01     X7.2 138714.91
## 1309 2002-01-01     X7.2 138754.84
## 1310 2002-02-01     X7.2 138774.26
## 1311 2002-03-01     X7.2 138793.67
## 1312 2002-04-01     X7.2 138685.55
## 1313 2002-05-01     X7.2 138577.43
## 1314 2002-06-01     X7.2 138185.44
## 1315 2002-07-01     X7.2 137793.45
## 1316 2002-08-01     X7.2 137292.86
## 1317 2002-09-01     X7.2 136792.26
## 1318 2002-10-01     X7.2 136507.09
## 1319 2002-11-01     X7.2 136221.93
## 1320 2002-12-01     X7.2 136162.04
## 1321 2003-01-01     X7.2 136102.16
## 1322 2003-02-01     X7.2 136093.92
## 1323 2003-03-01     X7.2 136085.69
## 1324 2003-04-01     X7.2 136172.62
## 1325 2003-05-01     X7.2 136259.56
## 1326 2003-06-01     X7.2 136327.28
## 1327 2003-07-01     X7.2 136395.01
## 1328 2003-08-01     X7.2 136397.72
## 1329 2003-09-01     X7.2 136400.43
## 1330 2003-10-01     X7.2 136358.83
## 1331 2003-11-01     X7.2 136317.22
## 1332 2003-12-01     X7.2 136344.40
## 1333 2004-01-01     X7.2 136371.59
## 1334 2004-02-01     X7.2 136556.39
## 1335 2004-03-01     X7.2 136741.20
## 1336 2004-04-01     X7.2 137115.03
## 1337 2004-05-01     X7.2 137488.87
## 1338 2004-06-01     X7.2 138082.01
## 1339 2004-07-01     X7.2 138675.16
## 1340 2004-08-01     X7.2 139298.16
## 1341 2004-09-01     X7.2 139921.16
## 1342 2004-10-01     X7.2 140217.52
## 1343 2004-11-01     X7.2 140513.89
## 1344 2004-12-01     X7.2 140550.68
## 1345 2005-01-01     X7.2 140587.47
## 1346 2005-02-01     X7.2 140522.37
## 1347 2005-03-01     X7.2 140457.26
## 1348 2005-04-01     X7.2 140236.33
## 1349 2005-05-01     X7.2 140015.39
## 1350 2005-06-01     X7.2 139448.38
## 1351 2005-07-01     X7.2 138881.36
## 1352 2005-08-01     X7.2 138317.66
## 1353 2005-09-01     X7.2 137753.96
## 1354 2005-10-01     X7.2 137610.52
## 1355 2005-11-01     X7.2 137467.08
## 1356 2005-12-01     X7.2 137417.75
## 1357 2006-01-01     X7.2 137368.42
## 1358 2006-02-01     X7.2 137326.68
## 1359 2006-03-01     X7.2 137284.93
## 1360 2006-04-01     X7.2 137397.00
## 1361 2006-05-01     X7.2 137509.07
## 1362 2006-06-01     X7.2 137510.18
## 1363 2006-07-01     X7.2 137511.28
## 1364 2006-08-01     X7.2 137076.41
## 1365 2006-09-01     X7.2 136641.54
## 1366 2006-10-01     X7.2 136116.96
## 1367 2006-11-01     X7.2 135592.39
## 1368 2006-12-01     X7.2 135354.12
## 1369 2007-01-01     X7.2 135115.86
## 1370 2007-02-01     X7.2 135022.77
## 1371 2007-03-01     X7.2 134929.69
## 1372 2007-04-01     X7.2 134854.60
## 1373 2007-05-01     X7.2 134779.51
## 1374 2007-06-01     X7.2 134894.44
## 1375 2007-07-01     X7.2 135009.37
## 1376 2007-08-01     X7.2 135426.85
## 1377 2007-09-01     X7.2 135844.32
## 1378 2007-10-01     X7.2 136277.29
## 1379 2007-11-01     X7.2 136710.25
## 1380 2007-12-01     X7.2 137000.68
## 1381 2008-01-01     X7.2 137291.11
## 1382 2008-02-01     X7.2 137578.40
## 1383 2008-03-01     X7.2 137865.69
## 1384 2008-04-01     X7.2 138209.90
## 1385 2008-05-01     X7.2 138554.12
## 1386 2008-06-01     X7.2 138731.73
## 1387 2008-07-01     X7.2 138909.33
## 1388 2008-08-01     X7.2 138784.71
## 1389 2008-09-01     X7.2 138660.09
## 1390 2008-10-01     X7.2 138397.53
## 1391 2008-11-01     X7.2 138134.97
## 1392 2008-12-01     X7.2 138004.08
## 1393 2009-01-01     X7.2 137873.20
## 1394 2009-02-01     X7.2 137809.72
## 1395 2009-03-01     X7.2 137746.25
## 1396 2009-04-01     X7.2 137949.81
## 1397 2009-05-01     X7.2 138153.36
## 1398 2009-06-01     X7.2 138548.13
## 1399 2009-07-01     X7.2 138942.89
## 1400 2009-08-01     X7.2 139269.88
## 1401 2009-09-01     X7.2 139596.87
## 1402 2009-10-01     X7.2 139621.03
## 1403 2009-11-01     X7.2 139645.19
## 1404 2009-12-01     X7.2 139521.78
## 1405 2010-01-01     X7.2 139398.36
## 1406 2010-02-01     X7.2 139231.39
## 1407 2010-03-01     X7.2 139064.41
## 1408 2010-04-01     X7.2 138894.26
## 1409 2010-05-01     X7.2 138724.10
## 1410 2010-06-01     X7.2 138440.21
## 1411 2010-07-01     X7.2 138156.33
## 1412 2010-08-01     X7.2 137967.79
## 1413 2010-09-01     X7.2 137779.25
## 1414 2010-10-01     X7.2 137855.30
## 1415 2010-11-01     X7.2 137931.35
## 1416 2010-12-01     X7.2 138151.46
## 1417 2011-01-01     X7.2 138371.56
## 1418 2011-02-01     X7.2 138300.06
## 1419 2011-03-01     X7.2 138228.56
## 1420 2011-04-01     X7.2 138069.06
## 1421 2011-05-01     X7.2 137909.55
## 1422 2011-06-01     X7.2 137787.68
## 1423 2011-07-01     X7.2 137665.82
## 1424 2011-08-01     X7.2 137533.37
## 1425 2011-09-01     X7.2 137400.91
## 1426 2011-10-01     X7.2 137165.31
## 1427 2011-11-01     X7.2 136929.71
## 1428 2011-12-01     X7.2 136893.58
## 1429 2012-01-01     X7.2 136857.45
## 1430 2012-02-01     X7.2 137145.30
## 1431 2012-03-01     X7.2 137433.14
## 1432 2012-04-01     X7.2 137890.87
## 1433 2012-05-01     X7.2 138348.61
## 1434 2012-06-01     X7.2 138864.48
## 1435 2012-07-01     X7.2 139380.36
## 1436 2012-08-01     X7.2 140058.72
## 1437 2012-09-01     X7.2 140737.08
## 1438 2012-10-01     X7.2 141162.26
## 1439 2012-11-01     X7.2 141587.44
## 1440 2012-12-01     X7.2 141627.04
## 1441 2013-01-01     X7.2 141666.63
## 1442 2013-02-01     X7.2 141406.42
## 1443 2013-03-01     X7.2 141146.20
## 1444 2013-04-01     X7.2 140663.02
## 1445 2013-05-01     X7.2 140179.84
## 1446 2013-06-01     X7.2 139805.36
## 1447 2013-07-01     X7.2 139430.88
## 1448 2013-08-01     X7.2 139116.73
## 1449 2013-09-01     X7.2 138802.58
## 1450 2013-10-01     X7.2 138531.02
## 1451 2013-11-01     X7.2 138259.46
## 1452 2013-12-01     X7.2 138220.50
## 1453 2014-01-01     X7.2 138181.55
## 1454 2014-02-01     X7.2 138297.16
## 1455 2014-03-01     X7.2 138412.76
## 1456 2014-04-01     X7.2 138616.75
## 1457 2014-05-01     X7.2 138820.74
## 1458 2014-06-01     X7.2 138901.64
## 1459 2014-07-01     X7.2 138982.53
## 1460 2014-08-01     X7.2 138729.32
## 1461 2014-09-01     X7.2 138476.11
## 1462 2014-10-01     X7.2 138303.58
## 1463 2014-11-01     X7.2 138131.06
## 1464 2014-12-01     X7.2 138078.91
## 1465 2015-01-01     X7.2 138026.77
## 1466 2015-02-01     X7.2 138008.45
## 1467 2015-03-01     X7.2 137990.13
## 1468 2015-04-01     X7.2 138004.97
## 1469 2015-05-01     X7.2 138019.81
## 1470 2015-06-01     X7.2 138148.95
## 1471 2015-07-01     X7.2 138278.09
## 1472 2015-08-01     X7.2 138608.18
## 1473 2015-09-01     X7.2 138938.27
## 1474 2015-10-01     X7.2 139202.87
## 1475 2015-11-01     X7.2 139467.47
## 1476 2015-12-01     X7.2 139424.11
## 1477 2016-01-01     X7.2 139380.75
## 1478 2016-02-01     X7.2 139230.96
## 1479 2016-03-01     X7.2 139081.16
## 1480 2016-04-01     X7.2 138853.60
## 1481 2016-05-01     X7.2 138626.05
## 1482 2016-06-01     X7.2 138389.51
## 1483 2016-07-01     X7.2 138152.97
## 1484 2016-08-01     X7.2 137965.89
## 1485 2016-09-01     X7.2 137778.82
## 1486 2016-10-01     X7.2 137671.63
## 1487 2016-11-01     X7.2 137564.45
## 1488 2016-12-01     X7.2 137565.96
## 1489 2017-01-01     X7.2 137567.47
## 1490 2017-02-01     X7.2 137514.51
## 1491 2017-03-01     X7.2 137461.55
## 1492 2017-04-01     X7.2 137209.78
## 1493 2017-05-01     X7.2 136958.01
## 1494 2017-06-01     X7.2 136678.36
## 1495 2017-07-01     X7.2 136398.71
## 1496 2017-08-01     X7.2 136098.15
## 1497 2017-09-01     X7.2 135797.60
## 1498 2017-10-01     X7.2 135464.30
## 1499 2017-11-01     X7.2 135130.99
## 1500 2017-12-01     X7.2 134768.86
## 1501 1993-01-01    X7.72 164659.23
## 1502 1993-02-01    X7.72 165001.91
## 1503 1993-03-01    X7.72 165344.59
## 1504 1993-04-01    X7.72 165654.33
## 1505 1993-05-01    X7.72 165964.08
## 1506 1993-06-01    X7.72 166263.91
## 1507 1993-07-01    X7.72 166563.74
## 1508 1993-08-01    X7.72 166847.91
## 1509 1993-09-01    X7.72 167132.09
## 1510 1993-10-01    X7.72 167108.45
## 1511 1993-11-01    X7.72 167084.80
## 1512 1993-12-01    X7.72 166813.28
## 1513 1994-01-01    X7.72 166541.76
## 1514 1994-02-01    X7.72 166275.18
## 1515 1994-03-01    X7.72 166008.60
## 1516 1994-04-01    X7.72 165607.63
## 1517 1994-05-01    X7.72 165206.67
## 1518 1994-06-01    X7.72 164853.41
## 1519 1994-07-01    X7.72 164500.16
## 1520 1994-08-01    X7.72 164385.43
## 1521 1994-09-01    X7.72 164270.71
## 1522 1994-10-01    X7.72 164391.30
## 1523 1994-11-01    X7.72 164511.90
## 1524 1994-12-01    X7.72 164621.84
## 1525 1995-01-01    X7.72 164731.78
## 1526 1995-02-01    X7.72 164876.12
## 1527 1995-03-01    X7.72 165020.45
## 1528 1995-04-01    X7.72 165242.50
## 1529 1995-05-01    X7.72 165464.55
## 1530 1995-06-01    X7.72 165818.98
## 1531 1995-07-01    X7.72 166173.42
## 1532 1995-08-01    X7.72 166574.90
## 1533 1995-09-01    X7.72 166976.37
## 1534 1995-10-01    X7.72 167180.97
## 1535 1995-11-01    X7.72 167385.57
## 1536 1995-12-01    X7.72 167415.42
## 1537 1996-01-01    X7.72 167445.27
## 1538 1996-02-01    X7.72 167352.72
## 1539 1996-03-01    X7.72 167260.18
## 1540 1996-04-01    X7.72 167190.56
## 1541 1996-05-01    X7.72 167120.93
## 1542 1996-06-01    X7.72 167045.96
## 1543 1996-07-01    X7.72 166970.99
## 1544 1996-08-01    X7.72 166618.39
## 1545 1996-09-01    X7.72 166265.78
## 1546 1996-10-01    X7.72 165908.96
## 1547 1996-11-01    X7.72 165552.14
## 1548 1996-12-01    X7.72 165402.27
## 1549 1997-01-01    X7.72 165252.40
## 1550 1997-02-01    X7.72 165090.24
## 1551 1997-03-01    X7.72 164928.08
## 1552 1997-04-01    X7.72 164444.90
## 1553 1997-05-01    X7.72 163961.72
## 1554 1997-06-01    X7.72 163608.91
## 1555 1997-07-01    X7.72 163256.11
## 1556 1997-08-01    X7.72 163531.69
## 1557 1997-09-01    X7.72 163807.26
## 1558 1997-10-01    X7.72 164049.53
## 1559 1997-11-01    X7.72 164291.79
## 1560 1997-12-01    X7.72 164224.57
## 1561 1998-01-01    X7.72 164157.35
## 1562 1998-02-01    X7.72 164095.44
## 1563 1998-03-01    X7.72 164033.53
## 1564 1998-04-01    X7.72 163837.94
## 1565 1998-05-01    X7.72 163642.36
## 1566 1998-06-01    X7.72 163499.37
## 1567 1998-07-01    X7.72 163356.39
## 1568 1998-08-01    X7.72 163427.71
## 1569 1998-09-01    X7.72 163499.02
## 1570 1998-10-01    X7.72 163799.31
## 1571 1998-11-01    X7.72 164099.60
## 1572 1998-12-01    X7.72 164460.57
## 1573 1999-01-01    X7.72 164821.54
## 1574 1999-02-01    X7.72 165409.18
## 1575 1999-03-01    X7.72 165996.82
## 1576 1999-04-01    X7.72 166530.87
## 1577 1999-05-01    X7.72 167064.93
## 1578 1999-06-01    X7.72 167097.18
## 1579 1999-07-01    X7.72 167129.43
## 1580 1999-08-01    X7.72 166911.47
## 1581 1999-09-01    X7.72 166693.52
## 1582 1999-10-01    X7.72 166712.75
## 1583 1999-11-01    X7.72 166731.98
## 1584 1999-12-01    X7.72 166658.88
## 1585 2000-01-01    X7.72 166585.77
## 1586 2000-02-01    X7.72 166522.25
## 1587 2000-03-01    X7.72 166458.73
## 1588 2000-04-01    X7.72 166641.49
## 1589 2000-05-01    X7.72 166824.26
## 1590 2000-06-01    X7.72 167171.15
## 1591 2000-07-01    X7.72 167518.04
## 1592 2000-08-01    X7.72 167718.79
## 1593 2000-09-01    X7.72 167919.53
## 1594 2000-10-01    X7.72 167948.70
## 1595 2000-11-01    X7.72 167977.86
## 1596 2000-12-01    X7.72 167926.67
## 1597 2001-01-01    X7.72 167875.48
## 1598 2001-02-01    X7.72 167635.80
## 1599 2001-03-01    X7.72 167396.12
## 1600 2001-04-01    X7.72 167105.48
## 1601 2001-05-01    X7.72 166814.84
## 1602 2001-06-01    X7.72 166676.06
## 1603 2001-07-01    X7.72 166537.29
## 1604 2001-08-01    X7.72 166579.45
## 1605 2001-09-01    X7.72 166621.61
## 1606 2001-10-01    X7.72 166683.41
## 1607 2001-11-01    X7.72 166745.22
## 1608 2001-12-01    X7.72 166770.85
## 1609 2002-01-01    X7.72 166796.49
## 1610 2002-02-01    X7.72 166808.75
## 1611 2002-03-01    X7.72 166821.02
## 1612 2002-04-01    X7.72 166664.68
## 1613 2002-05-01    X7.72 166508.34
## 1614 2002-06-01    X7.72 165993.92
## 1615 2002-07-01    X7.72 165479.51
## 1616 2002-08-01    X7.72 164853.37
## 1617 2002-09-01    X7.72 164227.24
## 1618 2002-10-01    X7.72 163901.86
## 1619 2002-11-01    X7.72 163576.49
## 1620 2002-12-01    X7.72 163507.85
## 1621 2003-01-01    X7.72 163439.21
## 1622 2003-02-01    X7.72 163446.27
## 1623 2003-03-01    X7.72 163453.33
## 1624 2003-04-01    X7.72 163590.89
## 1625 2003-05-01    X7.72 163728.46
## 1626 2003-06-01    X7.72 163811.28
## 1627 2003-07-01    X7.72 163894.11
## 1628 2003-08-01    X7.72 163873.35
## 1629 2003-09-01    X7.72 163852.58
## 1630 2003-10-01    X7.72 163809.04
## 1631 2003-11-01    X7.72 163765.49
## 1632 2003-12-01    X7.72 163803.21
## 1633 2004-01-01    X7.72 163840.92
## 1634 2004-02-01    X7.72 164046.84
## 1635 2004-03-01    X7.72 164252.75
## 1636 2004-04-01    X7.72 164703.18
## 1637 2004-05-01    X7.72 165153.62
## 1638 2004-06-01    X7.72 165898.53
## 1639 2004-07-01    X7.72 166643.44
## 1640 2004-08-01    X7.72 167407.39
## 1641 2004-09-01    X7.72 168171.33
## 1642 2004-10-01    X7.72 168499.92
## 1643 2004-11-01    X7.72 168828.50
## 1644 2004-12-01    X7.72 168849.96
## 1645 2005-01-01    X7.72 168871.42
## 1646 2005-02-01    X7.72 168775.09
## 1647 2005-03-01    X7.72 168678.76
## 1648 2005-04-01    X7.72 168379.05
## 1649 2005-05-01    X7.72 168079.34
## 1650 2005-06-01    X7.72 167390.13
## 1651 2005-07-01    X7.72 166700.92
## 1652 2005-08-01    X7.72 166031.04
## 1653 2005-09-01    X7.72 165361.17
## 1654 2005-10-01    X7.72 165187.17
## 1655 2005-11-01    X7.72 165013.18
## 1656 2005-12-01    X7.72 164954.76
## 1657 2006-01-01    X7.72 164896.35
## 1658 2006-02-01    X7.72 164881.44
## 1659 2006-03-01    X7.72 164866.52
## 1660 2006-04-01    X7.72 165078.29
## 1661 2006-05-01    X7.72 165290.07
## 1662 2006-06-01    X7.72 165343.73
## 1663 2006-07-01    X7.72 165397.40
## 1664 2006-08-01    X7.72 164892.78
## 1665 2006-09-01    X7.72 164388.16
## 1666 2006-10-01    X7.72 163771.63
## 1667 2006-11-01    X7.72 163155.11
## 1668 2006-12-01    X7.72 162845.67
## 1669 2007-01-01    X7.72 162536.23
## 1670 2007-02-01    X7.72 162365.28
## 1671 2007-03-01    X7.72 162194.33
## 1672 2007-04-01    X7.72 162043.19
## 1673 2007-05-01    X7.72 161892.05
## 1674 2007-06-01    X7.72 162015.06
## 1675 2007-07-01    X7.72 162138.06
## 1676 2007-08-01    X7.72 162718.47
## 1677 2007-09-01    X7.72 163298.88
## 1678 2007-10-01    X7.72 163906.59
## 1679 2007-11-01    X7.72 164514.30
## 1680 2007-12-01    X7.72 164922.03
## 1681 2008-01-01    X7.72 165329.75
## 1682 2008-02-01    X7.72 165692.53
## 1683 2008-03-01    X7.72 166055.31
## 1684 2008-04-01    X7.72 166409.46
## 1685 2008-05-01    X7.72 166763.61
## 1686 2008-06-01    X7.72 166924.50
## 1687 2008-07-01    X7.72 167085.39
## 1688 2008-08-01    X7.72 166890.91
## 1689 2008-09-01    X7.72 166696.42
## 1690 2008-10-01    X7.72 166313.36
## 1691 2008-11-01    X7.72 165930.30
## 1692 2008-12-01    X7.72 165752.68
## 1693 2009-01-01    X7.72 165575.05
## 1694 2009-02-01    X7.72 165512.06
## 1695 2009-03-01    X7.72 165449.06
## 1696 2009-04-01    X7.72 165771.02
## 1697 2009-05-01    X7.72 166092.98
## 1698 2009-06-01    X7.72 166629.41
## 1699 2009-07-01    X7.72 167165.85
## 1700 2009-08-01    X7.72 167582.61
## 1701 2009-09-01    X7.72 167999.37
## 1702 2009-10-01    X7.72 168104.85
## 1703 2009-11-01    X7.72 168210.33
## 1704 2009-12-01    X7.72 168116.94
## 1705 2010-01-01    X7.72 168023.54
## 1706 2010-02-01    X7.72 167845.78
## 1707 2010-03-01    X7.72 167668.01
## 1708 2010-04-01    X7.72 167455.75
## 1709 2010-05-01    X7.72 167243.48
## 1710 2010-06-01    X7.72 166874.75
## 1711 2010-07-01    X7.72 166506.01
## 1712 2010-08-01    X7.72 166254.34
## 1713 2010-09-01    X7.72 166002.67
## 1714 2010-10-01    X7.72 166034.03
## 1715 2010-11-01    X7.72 166065.39
## 1716 2010-12-01    X7.72 166262.48
## 1717 2011-01-01    X7.72 166459.56
## 1718 2011-02-01    X7.72 166295.08
## 1719 2011-03-01    X7.72 166130.59
## 1720 2011-04-01    X7.72 165862.99
## 1721 2011-05-01    X7.72 165595.40
## 1722 2011-06-01    X7.72 165390.70
## 1723 2011-07-01    X7.72 165186.00
## 1724 2011-08-01    X7.72 164986.71
## 1725 2011-09-01    X7.72 164787.42
## 1726 2011-10-01    X7.72 164491.89
## 1727 2011-11-01    X7.72 164196.36
## 1728 2011-12-01    X7.72 164164.86
## 1729 2012-01-01    X7.72 164133.37
## 1730 2012-02-01    X7.72 164486.75
## 1731 2012-03-01    X7.72 164840.14
## 1732 2012-04-01    X7.72 165398.98
## 1733 2012-05-01    X7.72 165957.82
## 1734 2012-06-01    X7.72 166620.98
## 1735 2012-07-01    X7.72 167284.14
## 1736 2012-08-01    X7.72 168176.58
## 1737 2012-09-01    X7.72 169069.01
## 1738 2012-10-01    X7.72 169612.20
## 1739 2012-11-01    X7.72 170155.40
## 1740 2012-12-01    X7.72 170206.94
## 1741 2013-01-01    X7.72 170258.48
## 1742 2013-02-01    X7.72 169949.90
## 1743 2013-03-01    X7.72 169641.33
## 1744 2013-04-01    X7.72 169095.05
## 1745 2013-05-01    X7.72 168548.77
## 1746 2013-06-01    X7.72 168245.98
## 1747 2013-07-01    X7.72 167943.20
## 1748 2013-08-01    X7.72 167747.36
## 1749 2013-09-01    X7.72 167551.52
## 1750 2013-10-01    X7.72 167324.12
## 1751 2013-11-01    X7.72 167096.71
## 1752 2013-12-01    X7.72 167072.93
## 1753 2014-01-01    X7.72 167049.15
## 1754 2014-02-01    X7.72 167166.80
## 1755 2014-03-01    X7.72 167284.44
## 1756 2014-04-01    X7.72 167427.75
## 1757 2014-05-01    X7.72 167571.06
## 1758 2014-06-01    X7.72 167465.55
## 1759 2014-07-01    X7.72 167360.04
## 1760 2014-08-01    X7.72 166921.78
## 1761 2014-09-01    X7.72 166483.52
## 1762 2014-10-01    X7.72 166294.83
## 1763 2014-11-01    X7.72 166106.15
## 1764 2014-12-01    X7.72 166054.20
## 1765 2015-01-01    X7.72 166002.25
## 1766 2015-02-01    X7.72 165955.75
## 1767 2015-03-01    X7.72 165909.26
## 1768 2015-04-01    X7.72 165920.29
## 1769 2015-05-01    X7.72 165931.33
## 1770 2015-06-01    X7.72 166128.17
## 1771 2015-07-01    X7.72 166325.01
## 1772 2015-08-01    X7.72 166802.79
## 1773 2015-09-01    X7.72 167280.57
## 1774 2015-10-01    X7.72 167679.07
## 1775 2015-11-01    X7.72 168077.56
## 1776 2015-12-01    X7.72 168089.21
## 1777 2016-01-01    X7.72 168100.85
## 1778 2016-02-01    X7.72 167918.56
## 1779 2016-03-01    X7.72 167736.26
## 1780 2016-04-01    X7.72 167365.12
## 1781 2016-05-01    X7.72 166993.97
## 1782 2016-06-01    X7.72 166564.50
## 1783 2016-07-01    X7.72 166135.02
## 1784 2016-08-01    X7.72 165791.47
## 1785 2016-09-01    X7.72 165447.93
## 1786 2016-10-01    X7.72 165268.49
## 1787 2016-11-01    X7.72 165089.06
## 1788 2016-12-01    X7.72 165097.07
## 1789 2017-01-01    X7.72 165105.07
## 1790 2017-02-01    X7.72 165065.69
## 1791 2017-03-01    X7.72 165026.32
## 1792 2017-04-01    X7.72 164734.75
## 1793 2017-05-01    X7.72 164443.18
## 1794 2017-06-01    X7.72 164123.19
## 1795 2017-07-01    X7.72 163803.19
## 1796 2017-08-01    X7.72 163449.32
## 1797 2017-09-01    X7.72 163095.46
## 1798 2017-10-01    X7.72 162692.67
## 1799 2017-11-01    X7.72 162289.89
## 1800 2017-12-01    X7.72 161847.87
## 1801 1993-01-01    X8.23 203655.93
## 1802 1993-02-01    X8.23 204133.64
## 1803 1993-03-01    X8.23 204611.35
## 1804 1993-04-01    X8.23 205044.50
## 1805 1993-05-01    X8.23 205477.65
## 1806 1993-06-01    X8.23 205896.29
## 1807 1993-07-01    X8.23 206314.93
## 1808 1993-08-01    X8.23 206731.50
## 1809 1993-09-01    X8.23 207148.07
## 1810 1993-10-01    X8.23 207232.51
## 1811 1993-11-01    X8.23 207316.96
## 1812 1993-12-01    X8.23 207040.05
## 1813 1994-01-01    X8.23 206763.14
## 1814 1994-02-01    X8.23 206421.38
## 1815 1994-03-01    X8.23 206079.61
## 1816 1994-04-01    X8.23 205543.89
## 1817 1994-05-01    X8.23 205008.17
## 1818 1994-06-01    X8.23 204646.27
## 1819 1994-07-01    X8.23 204284.37
## 1820 1994-08-01    X8.23 204284.29
## 1821 1994-09-01    X8.23 204284.22
## 1822 1994-10-01    X8.23 204472.21
## 1823 1994-11-01    X8.23 204660.21
## 1824 1994-12-01    X8.23 204810.95
## 1825 1995-01-01    X8.23 204961.69
## 1826 1995-02-01    X8.23 205148.22
## 1827 1995-03-01    X8.23 205334.75
## 1828 1995-04-01    X8.23 205544.87
## 1829 1995-05-01    X8.23 205754.98
## 1830 1995-06-01    X8.23 205934.96
## 1831 1995-07-01    X8.23 206114.94
## 1832 1995-08-01    X8.23 206298.36
## 1833 1995-09-01    X8.23 206481.79
## 1834 1995-10-01    X8.23 206572.02
## 1835 1995-11-01    X8.23 206662.24
## 1836 1995-12-01    X8.23 206663.62
## 1837 1996-01-01    X8.23 206665.00
## 1838 1996-02-01    X8.23 206547.16
## 1839 1996-03-01    X8.23 206429.32
## 1840 1996-04-01    X8.23 206506.11
## 1841 1996-05-01    X8.23 206582.91
## 1842 1996-06-01    X8.23 206846.94
## 1843 1996-07-01    X8.23 207110.96
## 1844 1996-08-01    X8.23 206928.38
## 1845 1996-09-01    X8.23 206745.80
## 1846 1996-10-01    X8.23 206337.21
## 1847 1996-11-01    X8.23 205928.62
## 1848 1996-12-01    X8.23 205714.98
## 1849 1997-01-01    X8.23 205501.35
## 1850 1997-02-01    X8.23 205220.40
## 1851 1997-03-01    X8.23 204939.45
## 1852 1997-04-01    X8.23 204148.29
## 1853 1997-05-01    X8.23 203357.12
## 1854 1997-06-01    X8.23 202745.29
## 1855 1997-07-01    X8.23 202133.45
## 1856 1997-08-01    X8.23 202486.57
## 1857 1997-09-01    X8.23 202839.69
## 1858 1997-10-01    X8.23 203190.44
## 1859 1997-11-01    X8.23 203541.19
## 1860 1997-12-01    X8.23 203468.04
## 1861 1998-01-01    X8.23 203394.89
## 1862 1998-02-01    X8.23 203342.08
## 1863 1998-03-01    X8.23 203289.28
## 1864 1998-04-01    X8.23 203044.18
## 1865 1998-05-01    X8.23 202799.07
## 1866 1998-06-01    X8.23 202589.60
## 1867 1998-07-01    X8.23 202380.12
## 1868 1998-08-01    X8.23 202411.95
## 1869 1998-09-01    X8.23 202443.77
## 1870 1998-10-01    X8.23 202759.46
## 1871 1998-11-01    X8.23 203075.16
## 1872 1998-12-01    X8.23 203501.93
## 1873 1999-01-01    X8.23 203928.71
## 1874 1999-02-01    X8.23 204675.14
## 1875 1999-03-01    X8.23 205421.57
## 1876 1999-04-01    X8.23 206081.77
## 1877 1999-05-01    X8.23 206741.96
## 1878 1999-06-01    X8.23 206785.97
## 1879 1999-07-01    X8.23 206829.98
## 1880 1999-08-01    X8.23 206606.69
## 1881 1999-09-01    X8.23 206383.40
## 1882 1999-10-01    X8.23 206477.89
## 1883 1999-11-01    X8.23 206572.38
## 1884 1999-12-01    X8.23 206479.58
## 1885 2000-01-01    X8.23 206386.79
## 1886 2000-02-01    X8.23 206260.90
## 1887 2000-03-01    X8.23 206135.01
## 1888 2000-04-01    X8.23 206436.71
## 1889 2000-05-01    X8.23 206738.42
## 1890 2000-06-01    X8.23 207325.35
## 1891 2000-07-01    X8.23 207912.27
## 1892 2000-08-01    X8.23 208236.93
## 1893 2000-09-01    X8.23 208561.59
## 1894 2000-10-01    X8.23 208613.08
## 1895 2000-11-01    X8.23 208664.56
## 1896 2000-12-01    X8.23 208615.29
## 1897 2001-01-01    X8.23 208566.01
## 1898 2001-02-01    X8.23 208237.15
## 1899 2001-03-01    X8.23 207908.28
## 1900 2001-04-01    X8.23 207419.98
## 1901 2001-05-01    X8.23 206931.69
## 1902 2001-06-01    X8.23 206586.04
## 1903 2001-07-01    X8.23 206240.39
## 1904 2001-08-01    X8.23 206214.03
## 1905 2001-09-01    X8.23 206187.68
## 1906 2001-10-01    X8.23 206244.79
## 1907 2001-11-01    X8.23 206301.90
## 1908 2001-12-01    X8.23 206341.17
## 1909 2002-01-01    X8.23 206380.44
## 1910 2002-02-01    X8.23 206394.35
## 1911 2002-03-01    X8.23 206408.27
## 1912 2002-04-01    X8.23 206188.29
## 1913 2002-05-01    X8.23 205968.31
## 1914 2002-06-01    X8.23 205296.73
## 1915 2002-07-01    X8.23 204625.14
## 1916 2002-08-01    X8.23 203806.16
## 1917 2002-09-01    X8.23 202987.19
## 1918 2002-10-01    X8.23 202538.52
## 1919 2002-11-01    X8.23 202089.86
## 1920 2002-12-01    X8.23 202002.54
## 1921 2003-01-01    X8.23 201915.22
## 1922 2003-02-01    X8.23 201970.75
## 1923 2003-03-01    X8.23 202026.28
## 1924 2003-04-01    X8.23 202313.59
## 1925 2003-05-01    X8.23 202600.89
## 1926 2003-06-01    X8.23 202820.74
## 1927 2003-07-01    X8.23 203040.60
## 1928 2003-08-01    X8.23 203051.17
## 1929 2003-09-01    X8.23 203061.74
## 1930 2003-10-01    X8.23 202970.05
## 1931 2003-11-01    X8.23 202878.36
## 1932 2003-12-01    X8.23 202882.51
## 1933 2004-01-01    X8.23 202886.65
## 1934 2004-02-01    X8.23 203086.23
## 1935 2004-03-01    X8.23 203285.80
## 1936 2004-04-01    X8.23 203733.31
## 1937 2004-05-01    X8.23 204180.82
## 1938 2004-06-01    X8.23 205061.21
## 1939 2004-07-01    X8.23 205941.61
## 1940 2004-08-01    X8.23 206947.80
## 1941 2004-09-01    X8.23 207953.99
## 1942 2004-10-01    X8.23 208420.13
## 1943 2004-11-01    X8.23 208886.27
## 1944 2004-12-01    X8.23 208920.84
## 1945 2005-01-01    X8.23 208955.40
## 1946 2005-02-01    X8.23 208894.31
## 1947 2005-03-01    X8.23 208833.21
## 1948 2005-04-01    X8.23 208581.22
## 1949 2005-05-01    X8.23 208329.22
## 1950 2005-06-01    X8.23 207491.79
## 1951 2005-07-01    X8.23 206654.36
## 1952 2005-08-01    X8.23 205752.29
## 1953 2005-09-01    X8.23 204850.22
## 1954 2005-10-01    X8.23 204585.16
## 1955 2005-11-01    X8.23 204320.10
## 1956 2005-12-01    X8.23 204198.13
## 1957 2006-01-01    X8.23 204076.15
## 1958 2006-02-01    X8.23 203987.72
## 1959 2006-03-01    X8.23 203899.30
## 1960 2006-04-01    X8.23 204076.77
## 1961 2006-05-01    X8.23 204254.24
## 1962 2006-06-01    X8.23 204288.65
## 1963 2006-07-01    X8.23 204323.05
## 1964 2006-08-01    X8.23 203677.35
## 1965 2006-09-01    X8.23 203031.65
## 1966 2006-10-01    X8.23 202258.24
## 1967 2006-11-01    X8.23 201484.84
## 1968 2006-12-01    X8.23 201106.04
## 1969 2007-01-01    X8.23 200727.24
## 1970 2007-02-01    X8.23 200531.73
## 1971 2007-03-01    X8.23 200336.21
## 1972 2007-04-01    X8.23 200219.60
## 1973 2007-05-01    X8.23 200103.00
## 1974 2007-06-01    X8.23 200405.13
## 1975 2007-07-01    X8.23 200707.27
## 1976 2007-08-01    X8.23 201546.67
## 1977 2007-09-01    X8.23 202386.08
## 1978 2007-10-01    X8.23 203186.03
## 1979 2007-11-01    X8.23 203985.99
## 1980 2007-12-01    X8.23 204518.12
## 1981 2008-01-01    X8.23 205050.25
## 1982 2008-02-01    X8.23 205548.88
## 1983 2008-03-01    X8.23 206047.51
## 1984 2008-04-01    X8.23 206480.18
## 1985 2008-05-01    X8.23 206912.86
## 1986 2008-06-01    X8.23 207017.90
## 1987 2008-07-01    X8.23 207122.95
## 1988 2008-08-01    X8.23 206832.07
## 1989 2008-09-01    X8.23 206541.19
## 1990 2008-10-01    X8.23 206064.98
## 1991 2008-11-01    X8.23 205588.77
## 1992 2008-12-01    X8.23 205361.82
## 1993 2009-01-01    X8.23 205134.87
## 1994 2009-02-01    X8.23 205021.88
## 1995 2009-03-01    X8.23 204908.89
## 1996 2009-04-01    X8.23 205260.77
## 1997 2009-05-01    X8.23 205612.65
## 1998 2009-06-01    X8.23 206256.99
## 1999 2009-07-01    X8.23 206901.32
## 2000 2009-08-01    X8.23 207378.32
## 2001 2009-09-01    X8.23 207855.32
## 2002 2009-10-01    X8.23 207936.76
## 2003 2009-11-01    X8.23 208018.19
## 2004 2009-12-01    X8.23 207887.57
## 2005 2010-01-01    X8.23 207756.95
## 2006 2010-02-01    X8.23 207577.38
## 2007 2010-03-01    X8.23 207397.80
## 2008 2010-04-01    X8.23 207147.21
## 2009 2010-05-01    X8.23 206896.61
## 2010 2010-06-01    X8.23 206398.48
## 2011 2010-07-01    X8.23 205900.35
## 2012 2010-08-01    X8.23 205531.12
## 2013 2010-09-01    X8.23 205161.88
## 2014 2010-10-01    X8.23 205134.50
## 2015 2010-11-01    X8.23 205107.11
## 2016 2010-12-01    X8.23 205290.02
## 2017 2011-01-01    X8.23 205472.93
## 2018 2011-02-01    X8.23 205278.20
## 2019 2011-03-01    X8.23 205083.47
## 2020 2011-04-01    X8.23 204849.14
## 2021 2011-05-01    X8.23 204614.80
## 2022 2011-06-01    X8.23 204450.37
## 2023 2011-07-01    X8.23 204285.94
## 2024 2011-08-01    X8.23 204085.49
## 2025 2011-09-01    X8.23 203885.04
## 2026 2011-10-01    X8.23 203584.83
## 2027 2011-11-01    X8.23 203284.61
## 2028 2011-12-01    X8.23 203286.34
## 2029 2012-01-01    X8.23 203288.08
## 2030 2012-02-01    X8.23 203721.44
## 2031 2012-03-01    X8.23 204154.80
## 2032 2012-04-01    X8.23 204880.87
## 2033 2012-05-01    X8.23 205606.93
## 2034 2012-06-01    X8.23 206551.54
## 2035 2012-07-01    X8.23 207496.15
## 2036 2012-08-01    X8.23 208812.84
## 2037 2012-09-01    X8.23 210129.52
## 2038 2012-10-01    X8.23 210969.18
## 2039 2012-11-01    X8.23 211808.84
## 2040 2012-12-01    X8.23 211933.60
## 2041 2013-01-01    X8.23 212058.36
## 2042 2013-02-01    X8.23 211632.22
## 2043 2013-03-01    X8.23 211206.08
## 2044 2013-04-01    X8.23 210365.68
## 2045 2013-05-01    X8.23 209525.27
## 2046 2013-06-01    X8.23 208889.49
## 2047 2013-07-01    X8.23 208253.70
## 2048 2013-08-01    X8.23 207802.07
## 2049 2013-09-01    X8.23 207350.44
## 2050 2013-10-01    X8.23 206965.77
## 2051 2013-11-01    X8.23 206581.10
## 2052 2013-12-01    X8.23 206552.68
## 2053 2014-01-01    X8.23 206524.27
## 2054 2014-02-01    X8.23 206737.59
## 2055 2014-03-01    X8.23 206950.91
## 2056 2014-04-01    X8.23 207244.21
## 2057 2014-05-01    X8.23 207537.52
## 2058 2014-06-01    X8.23 207483.98
## 2059 2014-07-01    X8.23 207430.44
## 2060 2014-08-01    X8.23 206913.25
## 2061 2014-09-01    X8.23 206396.06
## 2062 2014-10-01    X8.23 206226.97
## 2063 2014-11-01    X8.23 206057.88
## 2064 2014-12-01    X8.23 206061.46
## 2065 2015-01-01    X8.23 206065.04
## 2066 2015-02-01    X8.23 206003.64
## 2067 2015-03-01    X8.23 205942.23
## 2068 2015-04-01    X8.23 205883.52
## 2069 2015-05-01    X8.23 205824.81
## 2070 2015-06-01    X8.23 206025.20
## 2071 2015-07-01    X8.23 206225.60
## 2072 2015-08-01    X8.23 206813.41
## 2073 2015-09-01    X8.23 207401.23
## 2074 2015-10-01    X8.23 207890.71
## 2075 2015-11-01    X8.23 208380.20
## 2076 2015-12-01    X8.23 208395.43
## 2077 2016-01-01    X8.23 208410.65
## 2078 2016-02-01    X8.23 208241.17
## 2079 2016-03-01    X8.23 208071.68
## 2080 2016-04-01    X8.23 207658.05
## 2081 2016-05-01    X8.23 207244.43
## 2082 2016-06-01    X8.23 206624.88
## 2083 2016-07-01    X8.23 206005.34
## 2084 2016-08-01    X8.23 205447.29
## 2085 2016-09-01    X8.23 204889.24
## 2086 2016-10-01    X8.23 204621.87
## 2087 2016-11-01    X8.23 204354.50
## 2088 2016-12-01    X8.23 204348.65
## 2089 2017-01-01    X8.23 204342.79
## 2090 2017-02-01    X8.23 204297.50
## 2091 2017-03-01    X8.23 204252.20
## 2092 2017-04-01    X8.23 203888.00
## 2093 2017-05-01    X8.23 203523.80
## 2094 2017-06-01    X8.23 203087.82
## 2095 2017-07-01    X8.23 202651.85
## 2096 2017-08-01    X8.23 202170.96
## 2097 2017-09-01    X8.23 201690.07
## 2098 2017-10-01    X8.23 201142.60
## 2099 2017-11-01    X8.23 200595.13
## 2100 2017-12-01    X8.23 199987.57

4.1.1. TENDENCIA EN TODO EL PERIODO DE ESTUDIO: 1993 - 2017

Pasamos a dibujar las tendencias, primero en un único gráfico:

ggplot(fuel_speed_df_long, aes(x = date, y = value)) +
  geom_line(aes(color = variable), size = 1) +
  scale_colour_discrete() +
  labs(title = "Fuel consumption trends vs speed (I)", color="speeds") +
  ylab("fuel consumption, kg. (fuel oil) or m^3 (gas)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

A continuación las tendencias por separado:

ggplot(fuel_speed_df_long, aes(x = date, y = value)) +
  geom_line(aes(color = variable), size = 1) +
  facet_wrap(~variable, scales="free", ncol=2) +
  scale_colour_discrete() +
  labs(title = "Fuel consumption trends vs speed (II)", color="speeds") +
  ylab("fuel consumption, kg. (fuel oil) or m^3 (gas)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Se puede observar por las graficas de tendencia de consumo de fuel para las distintas velocidades, tanto la conjunta como por separado, que dichas tendencias guardan si no el mismo muy similar patrón a lo largo del tiempo, diferenciandose solo en los valores de combustible, que como era de esperar son mayores según aumenta la velocidad.

4.1.2. Máximo consumo de fuel: Enero 2013

which.max(fuel_speed_trends_df$X5.14)

## [1] 241

which.max(fuel_speed_trends_df$X6.69)

## [1] 241

which.max(fuel_speed_trends_df$X8.23)

## [1] 241

fuel_speed_trends_df$date[which.max(fuel_speed_trends_df$X8.23)]

## [1] "2013-01-01"

Comprobamos que el valor máximo exacto para todas las velocidades se corresponde con Enero de 2013

4.1.3. Periodo de valores altos de consumo de fuel: 1999 - mediados 2003

library(lubridate)

## Warning: package 'lubridate' was built under R version 3.6.2

## 
## Attaching package: 'lubridate'

## The following object is masked from 'package:base':
## 
##     date

period_high_fuel_consumpt <- fuel_speed_df_long %>%
  filter(year(date)>=1999 & year(date)<=2002)

ggplot(period_high_fuel_consumpt, aes(x = date, y = value)) +
  geom_line(aes(color = variable), size = 1) +
  facet_wrap(~variable, scales="free", ncol=2) +
  scale_colour_discrete() +
  labs(title = "Period of high fuel consumption: 1999 - 2003", color="speeds") +
  ylab("fuel consumption, kg. (fuel oil) or m^3 (gas)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

4.1.4. Periodo de mayor fluctuacion: 2005 - 2007

library(lubridate)


period_high_fluct_fuel_consumpt <- fuel_speed_df_long %>%
  filter(year(date)>=2004 & year(date)<=2007)

ggplot(period_high_fluct_fuel_consumpt, aes(x = date, y = value)) +
  geom_line(aes(color = variable), size = 1) +
  facet_wrap(~variable, scales="free", ncol=2) +
  scale_colour_discrete() +
  labs(title = "Period of greatest fluctuation: 2005 - 2008", color="speeds") +
  ylab("fuel consumption, kg. (fuel oil) or m^3 (gas)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

4.1.5. Descripción de las series temporales de consumo de fuel.

Ya se ha visto anteriormente la casi igualdad en las tendencias de consumo para las distintas velocidades. Pasamos a examinar las series temporales para 3 de las velocidades (mínima,intermedia,máxima):

descrp_fuel_ts <- ts(data = data.frame(speed_5.14=fuel_cons_speed_ts$`5.14`,speed_6.69=fuel_cons_speed_ts$`6.69`,speed_8.23=fuel_cons_speed_ts$`8.23`), start = 1993, frequency = 12)


ts_info(descrp_fuel_ts)

##  The descrp_fuel_ts series is a mts object with 3 variables and 300 observations
##  Frequency: 12 
##  Start time: 1993 1 
##  End time: 2017 12

ts_plot(descrp_fuel_ts,
title = "Fuel consumption (speed)",
type = "multiple")

Como observamos por las gráficas las series temporales para las distintas velocidades tienen un trazado prácticamente idéntico, diferenciandose claro esta en los valores de consumo de fuel (a mayor velocidad más consumo)

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(3,1))

spec_5.14 <- spec.pgram(fuel_cons_speed_ts$`5.14`,taper=0,log='no')

spec_6.69 <- spec.pgram(fuel_cons_speed_ts$`6.69`,taper=0,log='no')

spec_8.23 <- spec.pgram(fuel_cons_speed_ts$`8.23`,taper=0,log='no')

Resulta curioso observar que aparte del periodo anual predominante (al menos en 2) nos aparece otro periodo en distinto grado correspondiente a 2 años.

Completamos este apartado en cuanto a la estacionalidad y existencia de ciclos con las siguientes gráficas. En primer lugar un mapa de calor, en la que dada la similitud observada en las distintas series temporales de consumo por velocidad nos quedaremos para esta gráfica con dos velocidades, la mínima y la máxima.

ts_heatmap(fuel_cons_speed_ts$`5.14`, color = "Reds", title = "Fuel consumption (speed=5.14)")

ts_heatmap(fuel_cons_speed_ts$`8.23`, color = "Reds", title = "Fuel consumption (speed=8.23)")

Podemos observar señales de existencia de ciclo anual, con variaciones debidas quizás a las excepciones lógicas dado el rango de años u otros posibles factores puntuales influyentes (meteorológicos, etc.).

El consumo menor se corresponde con el mes de Julio, con valores bajos también en su anterior y posterior. Los valores más altos se concentran en general en los meses de Noviembre y Diciembre, con más excepciones.

• El comportamiento más uniforme en los meses de verano (menor consumo) y más cambiante en los meses de Noviembre a Enero, ennuesttro rango de estudio 1993-2017, se puede observar mejor en la siguiente gráfica del consumo a la velocidad intermedia (6.69 m/s):

ts_seasonal(fuel_cons_speed_ts$`6.69`,type ="box")

4.2. VARIABLES MESOCEÁNICAS.

4.2.1. U-component wind 10 meters

4.2.1.1. Distribución para todo el periodo de estudio. Boxplot. Outliers

u10_values_pts <- as.data.frame(u10.wind_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(u10_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot U-component wind 10 meters (points)",fill = "points") +
  xlab("points") +
  ylab("value (m/s)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Veamos a que fechas se corresponden los outliers. Probamos con el punto ‘1’:

box.u10 <- boxplot.stats(u10.wind_pts_ts$`1`)

out_values <- box.u10$out


out_index <- which(u10.wind_pts_ts$`1` %in% box.u10$out)


# get outliers year and month vectors, join and cast to Date

y <- as.character(floor(time(u10.wind_pts_ts$`1`)[out_index]))
m <- as.character(cycle(u10.wind_pts_ts$`1`)[out_index])

out_dates <- as.Date(paste(y,m,"01",sep = "-"))



data.frame(out_dates,out_values) 

##    out_dates out_values
## 1 2003-01-01   4.951956
## 2 2007-10-01  -5.404785
## 3 2010-12-01   5.106748

Realizada la prueba escribimos funcion para devolver los resultados en todos los puntos:

outliers_date_ts <- function(mesoc_var_pts_ts_list) {
  
  outliers_df <- function(tseries) {
    
    df <- data.frame()
    
    box <- boxplot.stats(tseries)
    
    out_values <- box$out
    
    out_index <- which(tseries %in% box$out)
    
    if (length(out_index) != 0) {
      
      # get outliers year and month vectors, join and cast to Date
      y <- as.character(floor(time(tseries)[out_index]))
      m <- as.character(cycle(tseries)[out_index])
      out_dates <- as.Date(paste(y,m,"01",sep = "-"))
      
      df <- data.frame(out_dates,out_values)
      
    }
    
    return(df)
    
  }
  
  
  return(lapply(mesoc_var_pts_ts_list,FUN = outliers_df)) 
  
  
}


outliers_date_ts(u10.wind_pts_ts)

## $`1`
##    out_dates out_values
## 1 2003-01-01   4.951956
## 2 2007-10-01  -5.404785
## 3 2010-12-01   5.106748
## 
## $`2`
##    out_dates out_values
## 1 2003-10-01  -4.004072
## 2 2004-01-01  10.585528
## 3 2006-03-01   8.956615
## 4 2007-02-01   9.014463
## 5 2010-02-01   9.559429
## 
## $`3`
##    out_dates out_values
## 1 1994-02-01   8.626285
## 2 2000-12-01  10.728352
## 3 2001-03-01   9.399051
## 4 2002-01-01   9.038799
## 5 2007-11-01  -2.881028
## 6 2008-11-01  -6.071032
## 7 2009-01-01   8.269623
## 8 2012-09-01  -3.126781
## 
## $`4`
##    out_dates out_values
## 1 2009-11-01   10.20413
## 2 2014-02-01   11.00004

NOTA: contrastar las fechas con periodos de valores altos y de máxima fluctuación

4.2.1.2. Análisis serie temporal.

descrp_u10_ts <- ts(data = data.frame(pnt_1=u10.wind_pts_ts$`1`,pnt_2=u10.wind_pts_ts$`2`,pnt_3=u10.wind_pts_ts$`3`,pnt_4=u10.wind_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_u10_ts, title = "U10-component wind (points)", type = "multiple")

Como era de esperar al ser distintos puntos geográficos los trazados de las series temporales no guardan similitud.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_u10.pt1 <- spec.pgram(u10.wind_pts_ts$`1`,taper=0,log='no')

spec_u10.pt2 <- spec.pgram(u10.wind_pts_ts$`2`,taper=0,log='no')

spec_u10.pt3 <- spec.pgram(u10.wind_pts_ts$`3`,taper=0,log='no')

spec_u10.pt4 <- spec.pgram(u10.wind_pts_ts$`4`,taper=0,log='no')

En los primeros dos puntos se observa la existencia de ciclo al año y 2 años. En las otras 2 se acompañan de otras componentes menores, en mayor grado en el punto 4.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(u10.wind_pts_ts$`1`, color = "Reds", title = "U10-component wind (pt. 1)")

ts_heatmap(u10.wind_pts_ts$`3`, color = "Reds", title = "U10-component wind (pt. 3)")

Sin haber patrón que pueda señalar la existencia de una componente mayoritaria anual, si podemos afirmar que en general los valores máximos se sulen encontrar en Enero y Febrero.

En cualquier caso y como se podía esperar para las variables mesoceánicas éstas presentan una mayor variación y espectogramas más complejos que no presentan una única componente (frecuencia).

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_u10_trends <- ts(data = data.frame(pnt_1=u10.wind_pts_trend$`1`,pnt_2=u10.wind_pts_trend$`2`,pnt_3=u10.wind_pts_trend$`3`,pnt_4=u10.wind_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_u10_trends, title = "U10-component wind and fuel consumption trends (points)", type = "multiple")

Las tendencias entre los puntos presentan distintos trazados como era esperable.

NOTA: COMPARAR CON LOS PERIODOS DE VALORES ALTOS Y DE MÁXIMA FLUCTUACIÓN, POR SI HAY ALGUNA RELACIÓN Primero de valores muy bajos (y distinta distribución como vimos al resto puntos) dificil comparación Resto (¿alta mar?) se observan algunos patrones.

4.2.1.3. Scatter plot: fuel consumption vs U-component wind 10 meters (points).

Dado que como hemos visto la tendencia del consumo de fuel para las distintas velocidades siguen un patrón muy similar, tomamos como referencia los valores (serie temporal) para el valor intermedio entre las velocidades (6.69 m/s.)

u10_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(u10_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot U-component wind 10 meters (points) vs. fuel consumption",color = "points") +
  xlab("U-component wind 10 meters [m/s]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Dispersión, no se visualiza recta posible

4.2.2. V-component wind 10 meters.

4.2.2.1. Boxplot. Outliers

v10_values_pts <- as.data.frame(v10.wind_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(v10_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot V-component wind 10 meters (points)",fill = "points") +
  xlab("points") +
  ylab("value (m/s)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar semejanzas, diferencias.

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(v10.wind_pts_ts)

## $`1`
##    out_dates out_values
## 1 2000-10-01  -5.239399
## 
## $`2`
##    out_dates out_values
## 1 2001-11-01  -3.205898
## 2 2017-04-01  -2.697417
## 
## $`3`
## data frame with 0 columns and 0 rows
## 
## $`4`
##    out_dates out_values
## 1 1993-01-01   4.597113
## 2 2002-01-01   5.492106
## 3 2012-04-01  -6.477585
## 4 2015-12-01   8.423544

Contrastar con periodos.

4.2.2.2. Análisis serie temporal.

descrp_v10_ts <- ts(data = data.frame(pnt_1=v10.wind_pts_ts$`1`,pnt_2=v10.wind_pts_ts$`2`,pnt_3=v10.wind_pts_ts$`3`,pnt_4=v10.wind_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_v10_ts, title = "v10-component wind (points)", type = "multiple")

Como era de esperar al ser distintos puntos geográficos los trazados de las series temporales no guardan similitud.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_v10.pt1 <- spec.pgram(v10.wind_pts_ts$`1`,taper=0,log='no')

spec_v10.pt2 <- spec.pgram(v10.wind_pts_ts$`2`,taper=0,log='no')

spec_v10.pt3 <- spec.pgram(v10.wind_pts_ts$`3`,taper=0,log='no')

spec_v10.pt4 <- spec.pgram(v10.wind_pts_ts$`4`, taper=0,log='no')

En este caso la componente a frecuencia 2 solo destaca en el punto 2 y algo menos en los 1 y 3

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(v10.wind_pts_ts$`1`, color = "Reds", title = "v10-component wind (pt. 1)")

ts_heatmap(v10.wind_pts_ts$`3`, color = "Reds", title = "v10-component wind (pt. 3)")

En el punto 1 con espectrograma mas plano si se observa cierta uniformidad anual, con valores altos positivos en Julio y extremos negativos en Noviembre y Diciembre.

En el segundo de espectrograma más complejo vemos como se pierde esta uniformidad.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_v10_trends <- ts(data = data.frame(pnt_1=v10.wind_pts_trend$`1`,pnt_2=v10.wind_pts_trend$`2`,pnt_3=v10.wind_pts_trend$`3`,pnt_4=v10.wind_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_v10_trends, title = "v10-component wind and fuel consumption trends (points)", type = "multiple")

NOTA: COMPARAR CON LOS PERIODOS DE VALORES ALTOS Y DE MÁXIMA FLUCTUACIÓN, POR SI HAY ALGUNA RELACIÓN Parece q no se observa relación

4.2.2.3. Scatter plot: fuel consumption vs V-component wind 10 meters (points).

v10_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(v10_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot V-component wind 10 meters (points) vs. fuel consumption",color = "points") +
  xlab("V-component wind 10 meters [m/s]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

En los 2 primeros puntos un mayor agrupamiento, dada la ausencia en los otros 2 no parece significativo.

4.2.3. Mean wave direction.

4.2.3.1. Boxplot. Outliers.

mwd_values_pts <- as.data.frame(m.wave.dir_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(mwd_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot Mean wave direction (points)",fill = "points") +
  xlab("points") +
  ylab("degrees relative North (clockwise)") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

NOTA: hablar de la concentración y diferencias

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(m.wave.dir_pts_ts)

## $`1`
##     out_dates out_values
## 1  1993-02-01   353.3390
## 2  1993-12-01   353.8554
## 3  1995-01-01   335.7270
## 4  1995-02-01   341.3194
## 5  1996-02-01   329.0360
## 6  1997-12-01   321.0870
## 7  2001-01-01   342.0445
## 8  2002-01-01   358.2172
## 9  2002-12-01   338.7484
## 10 2003-01-01   321.3067
## 11 2004-01-01   335.1832
## 12 2005-03-01   316.5549
## 13 2006-02-01   350.1748
## 14 2006-03-01   359.9312
## 15 2007-02-01   312.9731
## 16 2009-01-01   358.0030
## 17 2010-01-01   331.0466
## 18 2010-02-01   322.5153
## 19 2010-03-01   346.6260
## 20 2010-12-01   343.9782
## 21 2011-01-01   329.0525
## 22 2013-02-01   353.4379
## 23 2013-03-01   333.4417
## 24 2014-01-01   326.5420
## 25 2017-01-01   346.4228
## 
## $`2`
## data frame with 0 columns and 0 rows
## 
## $`3`
##     out_dates out_values
## 1  1999-02-01 219.600887
## 2  1999-11-01   7.641440
## 3  2000-03-01 202.741475
## 4  2001-11-01 131.991275
## 5  2003-10-01  20.490630
## 6  2004-10-01  12.096632
## 7  2005-02-01 159.486015
## 8  2005-11-01   5.235307
## 9  2006-08-01 165.440920
## 10 2007-11-01  22.655051
## 11 2008-09-01   3.823489
## 12 2008-11-01  70.541494
## 13 2010-11-01   6.487815
## 14 2010-12-01   9.047765
## 15 2011-05-01  21.012508
## 16 2011-06-01 222.622287
## 17 2012-09-01  16.062906
## 18 2013-05-01  37.350042
## 19 2014-12-01  75.853664
## 20 2017-04-01  27.115736
## 21 2017-11-01  11.613208
## 
## $`4`
##     out_dates  out_values
## 1  1993-02-01   5.0210624
## 2  1993-10-01  15.4805997
## 3  1995-06-01   6.6086707
## 4  1997-04-01  23.4406152
## 5  2001-12-01  24.1602577
## 6  2002-09-01   0.6592595
## 7  2005-02-01   2.6259162
## 8  2005-03-01 238.2182044
## 9  2007-09-01  28.6484100
## 10 2007-11-01  24.7755246
## 11 2009-09-01 356.5966547
## 12 2010-12-01  50.1717646
## 13 2017-04-01  18.6613098

Repasar fechas, Contrastar con periodos

4.2.3.2. Análisis serie temporal.

descrp_mwd_ts <- ts(data = data.frame(pnt_1=m.wave.dir_pts_ts$`1`,pnt_2=m.wave.dir_pts_ts$`2`,pnt_3=m.wave.dir_pts_ts$`3`,pnt_4=m.wave.dir_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_mwd_ts, title = "Mean wave direction (points)", type = "multiple")

Ptos 2 y 3 trazado similar (sin correspondecia temporal) se detecta concentración alrededor de 300 y outliers (boxplots)

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_mwd.pt1 <- spec.pgram(m.wave.dir_pts_ts$`1`,taper=0,log='no')

spec_mwd.pt2 <- spec.pgram(m.wave.dir_pts_ts$`2`,taper=0,log='no')

spec_mwd.pt3 <- spec.pgram(m.wave.dir_pts_ts$`3`,taper=0,log='no')

spec_mwd.pt4 <- spec.pgram(m.wave.dir_pts_ts$`4`,taper=0,log='no')

Espectros complejos puntos 3 y 4. Planos en el uno y 2, con la sorpresa para el primero de frecuencia 2 dominante.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(m.wave.dir_pts_ts$`1`, color = "Reds", title = "Mean wave direcction (pt. 1)")

ts_heatmap(m.wave.dir_pts_ts$`3`, color = "Reds", title = "Mean wave direcction (pt. 3)")

Como habiamos visto en el punto 1 se puede observar cierto patrón anual, con valores medios en Julio, bajos en Octubre y de forma menos uniforme extremos en Enero y Para el punto 3 con espectro mucho más complejo no es posible.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_mwd_trends <- ts(data = data.frame(pnt_1=m.wave.dir_pts_trend$`1`,pnt_2=m.wave.dir_pts_trend$`2`,pnt_3=m.wave.dir_pts_trend$`3`,pnt_4=m.wave.dir_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_mwd_trends, title = "v10-component wind and fuel consumption trends (points)", type = "multiple")

Contrastar con periodos de tiempo. No parece haber relación.

4.2.3.3. Scatter plot: fuel consumption vs Mean wave direction (points).

mwd_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(mwd_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot Mean wave direction (points) vs. fuel consumption",color = "points") +
  xlab("Mean wave direction [degrees relative North (clockwise)]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

INterpretar direccion respecto al gasto combustible, comentar agrupacion (anteriores conclusiones no generales)

4.2.4. Mean wave period.

4.2.4.1. Boxplot. Outliers.

mwp_values_pts <- as.data.frame(m.wave.period_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(mwp_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot Mean wave period (points)",fill = "points") +
  xlab("points") +
  ylab("period [s.]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar valores y diferencias

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(m.wave.period_pts_ts)

## $`1`
##    out_dates out_values
## 1 1995-09-01   9.024435
## 2 2003-09-01   8.441276
## 3 2009-03-01   8.426676
## 4 2017-09-01   9.265599
## 
## $`2`
## data frame with 0 columns and 0 rows
## 
## $`3`
## data frame with 0 columns and 0 rows
## 
## $`4`
## data frame with 0 columns and 0 rows

Pocos outliers y sin relacion (tiempos separados)

4.2.4.2. Análisis serie temporal.

descrp_mwp_ts <- ts(data = data.frame(pnt_1=m.wave.period_pts_ts$`1`,pnt_2=m.wave.period_pts_ts$`2`,pnt_3=m.wave.period_pts_ts$`3`,pnt_4=m.wave.period_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_mwp_ts, title = "Mean wave period (points)", type = "multiple")

Trazados similares para los puntos del 2 al 4,observandose cierta periodicidad.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_mwp.pt1 <- spec.pgram(m.wave.period_pts_ts$`1`,taper=0,log='no')

spec_mwp.pt2 <- spec.pgram(m.wave.period_pts_ts$`2`,taper=0,log='no')

spec_mwp.pt3 <- spec.pgram(m.wave.period_pts_ts$`3`,taper=0,log='no')

spec_mwp.pt4 <- spec.pgram(m.wave.period_pts_ts$`4`,taper=0,log='no')

Predominio claro en todas de la frecuencia 1. Como ya se había observado en el trazado (periodicidad clara), espectros planos en los puntos 2 al 4 exceptuando la frecuencia 1.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(m.wave.period_pts_ts$`1`, color = "Reds", title = "Mean wave period (pt. 1)")

ts_heatmap(m.wave.period_pts_ts$`3`, color = "Reds", title = "Mean wave period (pt. 3)")

En el punto 3 con espectro de frecuencia predominante observamos claro patrón anual, con extremos bajos en Julio y los altos en Diciembre y Enero.

Para el punto 1 de espectro algo más complejo el patrón no es tan claro

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_mwp_trends <- ts(data = data.frame(pnt_1=m.wave.period_pts_trend$`1`,pnt_2=m.wave.period_pts_trend$`2`,pnt_3=m.wave.period_pts_trend$`3`,pnt_4=m.wave.period_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_mwp_trends, title = "Mean wave period and fuel consumption trends (points)", type = "multiple")

Contrastar con periodos. Quizas patrón para periodo altos consumos.

4.2.4.3. Scatter plot: fuel consumption vs Mean wave period (points).

mwp_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(mwp_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot Mean wave period (points) vs. fuel consumption",color = "points") +
  xlab("Mean wave period [s.]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Aunque agrupacion a menos, parece cierta relacion lineal

4.2.5. Significant wave height.

4.2.5.1. Boxplot. Outliers.

swh_values_pts <- as.data.frame(sig.wave.height_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(swh_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot Significant wave height (points)",fill = "points") +
  xlab("points") +
  ylab("signf. wave height [m.]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar valores, diferencias

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(sig.wave.height_pts_ts)

## $`1`
## data frame with 0 columns and 0 rows
## 
## $`2`
## data frame with 0 columns and 0 rows
## 
## $`3`
## data frame with 0 columns and 0 rows
## 
## $`4`
##    out_dates out_values
## 1 2014-02-01   5.970439

Ausencia outliers

4.2.5.2. Análisis serie temporal.

descrp_swh_ts <- ts(data = data.frame(pnt_1=sig.wave.height_pts_ts$`1`,pnt_2=sig.wave.height_pts_ts$`2`,pnt_3=sig.wave.height_pts_ts$`3`,pnt_4=sig.wave.height_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_swh_ts, title = "Significant wave height (points)", type = "multiple")

Trazado con cierta similitud en los puntos 2 al 4, observandose señales de periodicidad.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_swh.pt1 <- spec.pgram(sig.wave.height_pts_ts$`1`,taper=0,log='no')

spec_swh.pt2 <- spec.pgram(sig.wave.height_pts_ts$`2`,taper=0,log='no')

spec_swh.pt3 <- spec.pgram(sig.wave.height_pts_ts$`3`,taper=0,log='no')

spec_swh.pt4 <- spec.pgram(sig.wave.height_pts_ts$`4`,taper=0,log='no')

Clara frecuencia dominante anual con resto plano, confirmando la periodicidad.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(sig.wave.height_pts_ts$`1`, color = "Reds", title = "Significant wave height (pt. 1)")

ts_heatmap(sig.wave.height_pts_ts$`3`, color = "Reds", title = "Significant wave height (pt. 3)")

En ambos se observa patrón anual, con extremos bajos en Julio y altos en Enero

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_swh_trends <- ts(data = data.frame(pnt_1=sig.wave.height_pts_trend$`1`,pnt_2=sig.wave.height_pts_trend$`2`,pnt_3=sig.wave.height_pts_trend$`3`,pnt_4=sig.wave.height_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_swh_trends, title = "Significant wave height and fuel consumption trends (points)", type = "multiple")

Periodo altos consumos, ptos 3 y 4, algo menos el 2. Priodo fluctuación solo pts 3 y 4

4.2.5.3. Scatter plot: fuel consumption vs Significant Wave Height (points).

swh_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(swh_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot Significant wave height (points) vs. fuel consumption",color = "points") +
  xlab("signf. wave height [m.]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Con agrupación a menos, parece cierta relacion lineal

4.2.6. Benjamin-Feir Index BFI

4.2.6.1. Boxplot. Outliers.

bfi_values_pts <- as.data.frame(bfi_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(bfi_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Boxplot BFI (points)",fill = "points") +
  xlab("points") +
  ylab("BFI [dimensionless]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

SEÑALAR VALORES BAJOS Y POCA VARIANZA, que ya se veian en el mapa de enero de 1993

No vale la pena analizar outliers

4.2.6.2. Análisis serie temporal.

descrp_bfi_ts <- ts(data = data.frame(pnt_1=bfi_pts_ts$`1`,pnt_2=bfi_pts_ts$`2`,pnt_3=bfi_pts_ts$`3`,pnt_4=bfi_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_bfi_ts, title = "BFI (points)", type = "multiple")

Dados los valores tan bajos (casi ruido) y su uniformidad (patente mapa) pasamos a examinar directamente la tendencia.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_bfi_trends <- ts(data = data.frame(pnt_1=bfi_pts_trend$`1`,pnt_2=bfi_pts_trend$`2`,pnt_3=bfi_pts_trend$`3`,pnt_4=bfi_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_bfi_trends, title = "BFI trend (points)", type = "multiple")

No se observa relación con periodos (no ayuda el infimo rango de valores de la variable)

4.2.6.3. Scatter plot: fuel consumption vs Benjamin-Feir Index BFI (points).

bfi_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(bfi_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "BFI (points) vs. fuel consumption",color = "points") +
  xlab("BFI [dimensionless]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar no se pueden sacar conclusiones.

4.2.7. Peak wave period

4.2.7.1. Boxplot. Outliers.

pwp_values_pts <- as.data.frame(peak.wave.period_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(pwp_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Peak wave period (points)",fill = "points") +
  xlab("points") +
  ylab("Peak wave period [s.]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar valores y diferencias

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(peak.wave.period_pts_ts)

## $`1`
##    out_dates out_values
## 1 1995-08-01  10.524878
## 2 1995-09-01  10.902210
## 3 1996-12-01  10.229273
## 4 1999-09-01  10.418808
## 5 2000-07-01   6.509428
## 6 2003-09-01  10.256442
## 7 2009-03-01  10.327518
## 8 2013-07-01   6.803511
## 9 2017-09-01  11.145867
## 
## $`2`
## data frame with 0 columns and 0 rows
## 
## $`3`
## data frame with 0 columns and 0 rows
## 
## $`4`
## data frame with 0 columns and 0 rows

Solo en el primer punto, agosto y septiembre 1995 (golfo mexico). Contrastar con periodos

4.2.7.2. Análisis serie temporal.

descrp_pwp_ts <- ts(data = data.frame(pnt_1=peak.wave.period_pts_ts$`1`,pnt_2=peak.wave.period_pts_ts$`2`,pnt_3=peak.wave.period_pts_ts$`3`,pnt_4=peak.wave.period_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_pwp_ts, title = "Peak wave period (points)", type = "multiple")

Se observa cierta semejanza en el trazado de los puntos 1 al 4. En los mismos también parec verse señales de cierta periodicidad.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_pwp.pt1 <- spec.pgram(peak.wave.period_pts_ts$`1`,taper=0,log='no')

spec_pwp.pt2 <- spec.pgram(peak.wave.period_pts_ts$`2`,taper=0,log='no')

spec_pwp.pt3 <- spec.pgram(peak.wave.period_pts_ts$`3`,taper=0,log='no')

spec_pwp.pt4 <- spec.pgram(peak.wave.period_pts_ts$`4`,taper=0,log='no')

Se comprueba periodicidad con frecuencia anual y resto espectro plano en los puntos 2 al 4. En el punto 1 predomina frecuencia anual con espectro más complejo.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(peak.wave.period_pts_ts$`1`, color = "Reds", title = "Peak wave period (pt. 1)")

ts_heatmap(peak.wave.period_pts_ts$`3`, color = "Reds", title = "Peak wave period (pt. 3)")

Para el punto 3 se comprueba periodicidad anual con valores extremos altos en diciembre y enero, y los bajos en Julio. En el pto 1 de espectro más complejo no queda claro.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_pwp_trends <- ts(data = data.frame(pnt_1=peak.wave.period_pts_trend$`1`,pnt_2=peak.wave.period_pts_trend$`2`,pnt_3=peak.wave.period_pts_trend$`3`,pnt_4=peak.wave.period_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_pwp_trends, title = "Peak wave period and fuel consumption trends (points)", type = "multiple")

Contrastar con periodos. Algo de coincidencia para el máximo

4.2.7.3. Scatter plot: fuel consumption vs Peak wave period (points).

pwp_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(pwp_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Peak wave period (points) vs. fuel consumption",color = "points") +
  xlab("Peak wave period [s.]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Concentracion a menos, parece cierta relacion lineal

4.2.8. Wave spectral kurtosis.

4.2.8.1. Boxplot. Outliers.

wsk_values_pts <- as.data.frame(wave.spectr.kurt_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(wsk_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Wave spectral kurtosis (points)",fill = "points") +
  xlab("points") +
  ylab("Wave spectral kurtosis [dimensionless]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Al igual que BFI, valores muy bajos y poca varianza. Recordar mapa de un solo color No vale la pena analizar outliers.

En cuanto al análisis temporal, al igual que con la variable BFI los valores muy bajos muy baja varianza hacen que la series temporales sean practicamente ruido, sin influencia clara.

4.2.8.2. Scatter plot: fuel consumption vs Wave spectral kurtosis (points).

wsk_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(wsk_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Wave spectral kurtosis (points) vs. fuel consumption",color = "points") +
  xlab("Wave spectral kurtosis [dimensionless]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Cortos valores y rangos, ptos muy dispersos.

4.2.9. Maximum individual wave height.

4.2.9.1. Boxplot. Outliers.

miwh_values_pts <- as.data.frame(max.indiv.wave.height_pts_ts) %>%
  mutate(year=as.character(floor(time(u10.wind_pts_ts$`1`)))) %>%
  mutate(month=as.character(cycle(u10.wind_pts_ts$`1`))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


ggplot(miwh_values_pts, aes(x = variable, y = value)) +
  geom_boxplot(aes(fill = variable)) +
  scale_fill_discrete() +
  labs(title = "Maximum individual wave height (points)",fill = "points") +
  xlab("points") +
  ylab("Max. individual wave height [m.]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Comentar valores y diferencias

Veamos a que fechas se corresponden los outliers:

outliers_date_ts(max.indiv.wave.height_pts_ts)

## $`1`
## data frame with 0 columns and 0 rows
## 
## $`2`
## data frame with 0 columns and 0 rows
## 
## $`3`
##    out_dates out_values
## 1 2000-12-01   10.28404
## 
## $`4`
##    out_dates out_values
## 1 2014-02-01   11.09553

Pocos outliers

4.2.9.2. Análisis serie temporal.

descrp_miwh_ts <- ts(data = data.frame(pnt_1=max.indiv.wave.height_pts_ts$`1`,pnt_2=max.indiv.wave.height_pts_ts$`2`,pnt_3=max.indiv.wave.height_pts_ts$`3`,pnt_4=max.indiv.wave.height_pts_ts$`4`), start = 1993, frequency = 12)


ts_plot(descrp_miwh_ts, title = "Max. Individual wave height (points)", type = "multiple")

De nuevo similitudes en el trazado en los puntos 2 al 4, y en mnor medida pero también para el primero. Se vislumbra la existencia de periodicidad en los primeros puntos nombrados.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_miwh.pt1 <- spec.pgram(max.indiv.wave.height_pts_ts$`1`,taper=0,log='no')

spec_miwh.pt2 <- spec.pgram(max.indiv.wave.height_pts_ts$`2`,taper=0,log='no')

spec_miwh.pt3 <- spec.pgram(max.indiv.wave.height_pts_ts$`3`,taper=0,log='no')

spec_miwh.pt4 <- spec.pgram(max.indiv.wave.height_pts_ts$`4`,taper=0,log='no')

Clara periodicidad anual en todos los puntos, con resto del espectro plano.

Vamos a observar el mapa de calor para los puntos 1 y 3, que presentan la mayor diferencia:

ts_heatmap(max.indiv.wave.height_pts_ts$`1`, color = "Reds", title = "Max. Individual wave height (points) (pt. 1)")

ts_heatmap(max.indiv.wave.height_pts_ts$`3`, color = "Reds", title = "Max. Individual wave height (points) (pt. 3)")

Patrón anual claro con extremos ionferiores en julio y los superiores en enero.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_miwh_trends <- ts(data = data.frame(pnt_1=max.indiv.wave.height_pts_trend$`1`,pnt_2=max.indiv.wave.height_pts_trend$`2`,pnt_3=max.indiv.wave.height_pts_trend$`3`,pnt_4=max.indiv.wave.height_pts_trend$`4`,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_miwh_trends, title = "Max. Individual wave height and fuel consumption trends (points)", type = "multiple")

Cierta correspondencia en el periodo de consumos altos y en el máximo (ptos 2 al 4 y 3 y 4 respectivamente).

4.2.9.3. Scatter plot: fuel consumption vs maximum individual wave height (points).

miwh_values_pts$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(miwh_values_pts, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Maximum individual wave height (points) vs. fuel consumption",color = "points") +
  xlab("Max. individual wave height [m.]") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Concentracion a menos, parece cierta relación lineal.

4.3. RELACIÓN CONSUMO DE FUEL Y VARIABLES MESOCEÁNICAS: MATRIZ DE CORRELACIÓN, PCA.

Para este punto necesitamos tener los datos por punto, un dataframe para cada punto con el valor de todas las variables. Eliminamos las variables “Benjamin Feir Index (BFI)” y “Wave spectral kurtosis” a raíz de los resultados del punto anterior en el que comprobamos que tienen varianza cercana a cero.

Ptrimero inicializamos las variables necesarias para el proceso

n_points <- 4
n_data <- 300

vars_mesoc_ts <- list(u10.wind_pts_ts,v10.wind_pts_ts,m.wave.dir_pts_ts,m.wave.period_pts_ts,sig.wave.height_pts_ts,peak.wave.period_pts_ts,max.indiv.wave.height_pts_ts)


names_vars_mesoc_ts <- c("u10_wind","v10_wind","mean_wave_direct","mean_wave_period","signf_wave_height","peak_wave_period","max_indiv_wv_height")


df_pt1 <- data.frame(idx_time=1:n_data)
df_pt2 <- data.frame(idx_time=1:n_data)
df_pt3 <- data.frame(idx_time=1:n_data)
df_pt4 <- data.frame(idx_time=1:n_data)



df_points_list <- list(df_pt1,df_pt2,df_pt3,df_pt4)

Finalmente recorremos cada variable (lista con los valores para los 4 puntos) y vamos guardando los valores de cada punto en su dataframe correspondiente:

for (nvar in 1:length(names_vars_mesoc_ts)) {
  
  m_name <- names_vars_mesoc_ts[nvar]
  m_var <- vars_mesoc_ts[[nvar]]
  
  
  for (npoint in 1:n_points) {
    
    
    df_points_list[[npoint]][m_name] <- m_var[[npoint]]
    
    
    
    
    
  }
  
  
}


str(df_points_list)

## List of 4
##  $ :'data.frame':    300 obs. of  8 variables:
##   ..$ idx_time           : int [1:300] 1 2 3 4 5 6 7 8 9 10 ...
##   ..$ u10_wind           : Time-Series [1:300] from 1993 to 2018: -1.68 2.25 1.13 1.01 -1.54 ...
##   ..$ v10_wind           : Time-Series [1:300] from 1993 to 2018: 1.454 -0.638 0.88 -0.572 0.792 ...
##   ..$ mean_wave_direct   : Time-Series [1:300] from 1993 to 2018: 86.1 353.3 17.1 27.6 91 ...
##   ..$ mean_wave_period   : Time-Series [1:300] from 1993 to 2018: 7.54 7.41 7.56 7.21 7.39 ...
##   ..$ signf_wave_height  : Time-Series [1:300] from 1993 to 2018: 2.2 2.25 2.41 1.95 1.29 ...
##   ..$ peak_wave_period   : Time-Series [1:300] from 1993 to 2018: 9.03 8.59 8.92 8.52 9.06 ...
##   ..$ max_indiv_wv_height: Time-Series [1:300] from 1993 to 2018: 4.17 4.28 4.57 3.71 2.44 ...
##  $ :'data.frame':    300 obs. of  8 variables:
##   ..$ idx_time           : int [1:300] 1 2 3 4 5 6 7 8 9 10 ...
##   ..$ u10_wind           : Time-Series [1:300] from 1993 to 2018: 4.7748 1.7727 2.4426 0.0225 0.4191 ...
##   ..$ v10_wind           : Time-Series [1:300] from 1993 to 2018: 0.696 3.928 2.594 1.848 2.548 ...
##   ..$ mean_wave_direct   : Time-Series [1:300] from 1993 to 2018: 296.6 274.5 255.5 10.2 36.1 ...
##   ..$ mean_wave_period   : Time-Series [1:300] from 1993 to 2018: 8.39 8.2 8.18 7.96 7.9 ...
##   ..$ signf_wave_height  : Time-Series [1:300] from 1993 to 2018: 3.05 2.9 2.9 2.46 2.12 ...
##   ..$ peak_wave_period   : Time-Series [1:300] from 1993 to 2018: 9.75 9.72 9.46 9.32 9.27 ...
##   ..$ max_indiv_wv_height: Time-Series [1:300] from 1993 to 2018: 5.74 5.45 5.46 4.66 4.01 ...
##  $ :'data.frame':    300 obs. of  8 variables:
##   ..$ idx_time           : int [1:300] 1 2 3 4 5 6 7 8 9 10 ...
##   ..$ u10_wind           : Time-Series [1:300] from 1993 to 2018: 4.74 -2.03 2.95 1.17 1.53 ...
##   ..$ v10_wind           : Time-Series [1:300] from 1993 to 2018: 1.304 0.549 -1.312 1.323 -2.442 ...
##   ..$ mean_wave_direct   : Time-Series [1:300] from 1993 to 2018: 292 322 328 312 357 ...
##   ..$ mean_wave_period   : Time-Series [1:300] from 1993 to 2018: 9.8 8.66 9.56 8.82 8.52 ...
##   ..$ signf_wave_height  : Time-Series [1:300] from 1993 to 2018: 3.81 2.85 3.53 2.7 2.51 ...
##   ..$ peak_wave_period   : Time-Series [1:300] from 1993 to 2018: 11.6 10.5 11.4 10.8 10.3 ...
##   ..$ max_indiv_wv_height: Time-Series [1:300] from 1993 to 2018: 7.09 5.35 6.6 5.05 4.71 ...
##  $ :'data.frame':    300 obs. of  8 variables:
##   ..$ idx_time           : int [1:300] 1 2 3 4 5 6 7 8 9 10 ...
##   ..$ u10_wind           : Time-Series [1:300] from 1993 to 2018: 4.3882 -5.2959 -0.9756 4.8805 -0.0784 ...
##   ..$ v10_wind           : Time-Series [1:300] from 1993 to 2018: 4.597 -3.183 1 -2.79 -0.637 ...
##   ..$ mean_wave_direct   : Time-Series [1:300] from 1993 to 2018: 279.4 5.02 302.83 304.78 329.06 ...
##   ..$ mean_wave_period   : Time-Series [1:300] from 1993 to 2018: 10.61 9.07 10 8.94 7.93 ...
##   ..$ signf_wave_height  : Time-Series [1:300] from 1993 to 2018: 4.09 2.64 3.32 3.22 2.31 ...
##   ..$ peak_wave_period   : Time-Series [1:300] from 1993 to 2018: 12.87 11.19 11.87 10.92 9.69 ...
##   ..$ max_indiv_wv_height: Time-Series [1:300] from 1993 to 2018: 7.6 4.96 6.18 6.05 4.36 ...

Comprobamos que se ha realizado bien la carga de los dataframe de cada punto con una de las variables:

str(u10.wind_pts_ts)

## List of 4
##  $ 1: Time-Series [1:300] from 1993 to 2018: -1.68 2.25 1.13 1.01 -1.54 ...
##  $ 2: Time-Series [1:300] from 1993 to 2018: 4.7748 1.7727 2.4426 0.0225 0.4191 ...
##  $ 3: Time-Series [1:300] from 1993 to 2018: 4.74 -2.03 2.95 1.17 1.53 ...
##  $ 4: Time-Series [1:300] from 1993 to 2018: 4.3882 -5.2959 -0.9756 4.8805 -0.0784 ...

4.3.1. MATRIZ DE CORRELACIÓN PARA CADA PUNTO GEOGRÁFICO

Vamos a calcular la matriz de correlación para los dataframes con las variables de cada punto, a la que añadimos como nueva variable el consumo de fuel para la velocidad que anteriormente hemos escogido de referencia (6.69 m/s).

PRIMER PUNTO.

df1 <- df_points_list[[1]] %>%
  select(-idx_time) %>%
  mutate(fuel_consump=fuel_cons_speed_ts$`6.69`)

mtrx_cor1 <- cor(df1)

mtrx_cor1

##                        u10_wind   v10_wind mean_wave_direct
## u10_wind             1.00000000  0.1933377       0.49149006
## v10_wind             0.19333766  1.0000000       0.19249197
## mean_wave_direct     0.49149006  0.1924920       1.00000000
## mean_wave_period    -0.10286976 -0.5649742      -0.14125309
## signf_wave_height    0.09154718 -0.6461760       0.01501317
## peak_wave_period    -0.14620597 -0.4540390      -0.16690738
## max_indiv_wv_height  0.10013025 -0.6419378       0.02131613
## fuel_consump        -0.31812031 -0.6433532      -0.26081642
##                     mean_wave_period signf_wave_height peak_wave_period
## u10_wind                  -0.1028698        0.09154718       -0.1462060
## v10_wind                  -0.5649742       -0.64617600       -0.4540390
## mean_wave_direct          -0.1412531        0.01501317       -0.1669074
## mean_wave_period           1.0000000        0.71428655        0.9269852
## signf_wave_height          0.7142865        1.00000000        0.5402925
## peak_wave_period           0.9269852        0.54029251        1.0000000
## max_indiv_wv_height        0.7026276        0.99980506        0.5276190
## fuel_consump               0.5313981        0.52349202        0.4642619
##                     max_indiv_wv_height fuel_consump
## u10_wind                     0.10013025   -0.3181203
## v10_wind                    -0.64193783   -0.6433532
## mean_wave_direct             0.02131613   -0.2608164
## mean_wave_period             0.70262762    0.5313981
## signf_wave_height            0.99980506    0.5234920
## peak_wave_period             0.52761901    0.4642619
## max_indiv_wv_height          1.00000000    0.5184317
## fuel_consump                 0.51843170    1.0000000

Podremos sacar más facilmente conclusiones con la gráfica:

library(corrplot)

## Warning: package 'corrplot' was built under R version 3.6.2

corrplot(mtrx_cor1, method = "shade", shade.col = NA, addCoef.col = TRUE, tl.col = "black", tl.srt = 45)

En primer lugar observamos una muy alta correlación (0.93) entre las variables “peak_wave_period” y “mean_”wave_period“. Y con total rotundidad entre las dos relativas de altura”signf_wave_height" y “max_indiv_wv_height”, que llega a la unidad. Estos nos llevaría a prescindir de alguna en cada par a la hora de aplicar PCA. Dejamos la elección a después de ver los resultados en los puntos restantes.

En cuanto al consumo de combustible, sin llegar a ser altas vemos correlacion negativa para “la componente vertical (hacia el norte) del viento”v10_wind" y positivas por orden decreciente para “mean_wave_period”, “signif_wave_height” y “max_indiv_wv_height”.

SEGUNDO PUNTO.

df2 <- df_points_list[[2]] %>%
  select(-idx_time) %>%
  mutate(fuel_consump=fuel_cons_speed_ts$`6.69`)

mtrx_cor2 <- cor(df2)


corrplot(mtrx_cor2, method = "shade", shade.col = NA, addCoef.col = TRUE, tl.col = "black", tl.srt = 45)

• corr entre variables: ademas de las nombradas se suman las de altura con periodicidad de las olas.

• corr con fuel: las mismas anteriores pero con ligero descenso, más acuciado en las de altura

TERCER PUNTO.

df3 <- df_points_list[[3]] %>%
  select(-idx_time) %>%
  mutate(fuel_consump=fuel_cons_speed_ts$`6.69`)

mtrx_cor3 <- cor(df3)


corrplot(mtrx_cor3, method = "shade", shade.col = NA, addCoef.col = TRUE, tl.col = "black", tl.srt = 45)

• corr entre variables: las mismas, más alta todavía entre altura y periodo de las olas.

• corr con fuel: desaparece como a considerar la componente de viento. Las restantes mas parecidas al primer punto.

CUARTO PUNTO.

df4 <- df_points_list[[4]] %>%
  select(-idx_time) %>%
  mutate(fuel_consump=fuel_cons_speed_ts$`6.69`)

mtrx_cor4 <- cor(df4)


corrplot(mtrx_cor4, method = "shade", shade.col = NA, addCoef.col = TRUE, tl.col = "black", tl.srt = 45)

• corr entre variables: IGUAL PUNTO ANTERIOR

• corr con fuel: desaparece como a considerar la componente de viento. Sin grandes cambio resto.

4.3.2. PCA

A cada uno de los dataframes de cada punto le aplicamos PCA. Eliminamos antes las variables “signf_wave_height” y “peak_wave_period”, quedándonos con “max_indiv_wv_height” y “mean_wave_period”, por su muy alta correlación.

4.3.2.1. REDUCCION PCA Y SU TENDENCIA, PUNTO 1

df1pca <- df1 %>%
  select(-fuel_consump,-signf_wave_height,-peak_wave_period)

pca1 <- prcomp(df1pca)

summary(pca1)

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5
## Standard deviation     78.717 1.7546 1.60127 0.58477 0.30790
## Proportion of Variance  0.999 0.0005 0.00041 0.00006 0.00002
## Cumulative Proportion   0.999 0.9995 0.99993 0.99998 1.00000

Observamos que ya con la primera componente conservamos prácticamente la totalidad de la varianza (99.9%)

reducc_pca1_ts <- ts(pca1$x[,1], start = 1993, frequency=12)

reducc_pca1_ts.dc <- stl(reducc_pca1_ts, s.window = "periodic", na.action = na.omit)
    
reducc_pca1_trend <- reducc_pca1_ts.dc$time.series[,"trend"]

plot(reducc_pca1_ts.dc)

4.3.2.2. REDUCCION PCA Y SU TENDENCIA, PUNTO 2

df2pca <- df2 %>%
  select(-fuel_consump,-signf_wave_height,-peak_wave_period)

pca2 <- prcomp(df2pca)

summary(pca2)

## Importance of components:
##                             PC1     PC2     PC3     PC4     PC5
## Standard deviation     109.2403 2.17168 1.68889 0.97775 0.27244
## Proportion of Variance   0.9993 0.00039 0.00024 0.00008 0.00001
## Cumulative Proportion    0.9993 0.99967 0.99991 0.99999 1.00000

reducc_pca2_ts <- ts(pca2$x[,1], start = 1993, frequency=12)

reducc_pca2_ts.dc <- stl(reducc_pca2_ts, s.window = "periodic", na.action = na.omit)
    
reducc_pca2_trend <- reducc_pca2_ts.dc$time.series[,"trend"]

plot(reducc_pca2_ts.dc)

4.3.2.3. REDUCCION PCA Y SU TENDENCIA, PUNTO 3

df3pca <- df3 %>%
  select(-fuel_consump,-signf_wave_height,-peak_wave_period)

pca3 <- prcomp(df3pca)

summary(pca3)

## Importance of components:
##                            PC1    PC2     PC3     PC4     PC5
## Standard deviation     66.7888 2.5908 1.83202 1.47257 0.29412
## Proportion of Variance  0.9972 0.0015 0.00075 0.00048 0.00002
## Cumulative Proportion   0.9972 0.9988 0.99950 0.99998 1.00000

reducc_pca3_ts <- ts(pca3$x[,1], start = 1993, frequency=12)

reducc_pca3_ts.dc <- stl(reducc_pca3_ts, s.window = "periodic", na.action = na.omit)
    
reducc_pca3_trend <- reducc_pca3_ts.dc$time.series[,"trend"]

plot(reducc_pca3_ts.dc)

4.3.2.4. REDUCCION PCA Y SU TENDENCIA, PUNTO 4

df4pca <- df4 %>%
  select(-fuel_consump,-signf_wave_height,-peak_wave_period)

pca4 <- prcomp(df4pca)

summary(pca4)

## Importance of components:
##                            PC1     PC2     PC3     PC4     PC5
## Standard deviation     57.1322 3.07180 1.87621 1.44639 0.36251
## Proportion of Variance  0.9954 0.00288 0.00107 0.00064 0.00004
## Cumulative Proportion   0.9954 0.99825 0.99932 0.99996 1.00000

reducc_pca4_ts <- ts(pca4$x[,1], start = 1993, frequency=12)

reducc_pca4_ts.dc <- stl(reducc_pca4_ts, s.window = "periodic", na.action = na.omit)
    
reducc_pca4_trend <- reducc_pca4_ts.dc$time.series[,"trend"]

plot(reducc_pca4_ts.dc)

4.3.2.5. Scatterplot reduccion PCA vs consumo de fuel.

pca_vs_fuel <- data.frame(pca_1=reducc_pca1_ts,pca_2=reducc_pca2_ts,pca_3=reducc_pca3_ts,pca_4=reducc_pca4_ts) %>%
  mutate(year=as.character(floor(time(reducc_pca1_ts)))) %>%
  mutate(month=as.character(cycle(reducc_pca1_ts))) %>%
  mutate(day="01") %>%
  unite(date,year,month,day,sep = "-") %>%
  mutate(date=as.Date(date)) %>%
  select(date,everything()) %>%
  gather(key = "variable", value = "value", -date)


pca_vs_fuel$fuel_ref <- fuel_cons_speed_ts$`6.69`


ggplot(pca_vs_fuel, aes(x = value,group = variable,color=variable)) +
  geom_point(aes(y=fuel_ref)) +
  facet_wrap( ~ variable, ncol = 2) +
  scale_color_discrete() +
  labs(title = "Scatter plot Reducc. PCA (points) vs. fuel consumption",color = "points") +
  xlab("Reducc. PCA") +
  ylab("fuel consumption (speed = 6.69 m/s) [kg or m^3]") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

Exceptuando en el punto 2, donde los puntos de la gráfica están mas dispersos, se observa cierta relación lineal con pendiente negativa, llegando a ser casi vertical en el punto 4.

4.3.2.6. Análisis serie temporal (reducción PCA)

descrp_pca_ts <- ts(data = data.frame(pnt_1=reducc_pca1_ts,pnt_2=reducc_pca2_ts,pnt_3=reducc_pca3_ts,pnt_4=reducc_pca4_ts), start = 1993, frequency = 12)


ts_plot(descrp_miwh_ts, title = "PCA (points)", type = "multiple")

Se observa alguna semejanza en el trazado para los 4 puntos y la posible existencia de periodicidad menos clara en el primero.

Estacionalidad, existencia de ciclos.

En cuanto a la estacionalidad pasamos a examinar el periodograma de las tres:

par(mfrow=c(4,1))

spec_pca.pt1 <- spec.pgram(reducc_pca1_ts,taper=0,log='no')

spec_pca.pt2 <- spec.pgram(reducc_pca2_ts,taper=0,log='no')

spec_pca.pt3 <- spec.pgram(reducc_pca3_ts, taper=0,log='no')

spec_pca.pt4 <- spec.pgram(reducc_pca4_ts, taper=0,log='no')

Espectro con periodicidad predominante en los dos primeros, con la sorpresa de ser para la frecuencia2 el primero. Espectros mucho más complejos en los otros dos puntos con lo cual no hay componente de frecuencia clara.

Vamos a hacer el mapa de calor en este caso para los puntos 2 y 3 (más dispares y el segundo en principio con frecuencia anual)

ts_heatmap(reducc_pca2_ts, color = "Reds", title = "PCA (pt. 2)")

ts_heatmap(reducc_pca3_ts, color = "Reds", title = "PCA (pt. 3)")

En el punto 2 se observa uniformidad en los valores para los meses de Julio y Enero, y presencia mayoritaria de valores extremos en Septiembre, que señalarían la frecuencia anual vista en el spectrograma

No se puede detectar un claro patrón en el punto 3, con predominio de valores bajos para casi todos los meses.

Trend component (points)

Vamos a contrastar las tendencias entre los puntos y con el consumo de fuel (tomamos como valor de velocidad el intermedio)

descrp_pca_trends <- ts(data = data.frame(pnt_1=reducc_pca1_trend,pnt_2=reducc_pca2_trend,pnt_3=reducc_pca3_trend,pnt_4=reducc_pca4_trend,fuel_consumpt=fuel_cons_speed_trends$`6.69`), start = 1993, frequency = 12)


ts_plot(descrp_pca_trends, title = "PCA (points) and fuel consumption trends ", type = "multiple")

Solo se observa correspondencia alguna correspondencia con el máximo en los 3 primeos puntos